Archive:Inverse semigroup - Revision history

wikademia>Wikademia: Text replace - 'w:' to 'Wikipedia:'

2009-04-11T18:20:24Z

Text replace - 'w:' to 'Wikipedia:'

← Older revision		Revision as of 18:20, 11 April 2009
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	*{{cite journal \| author=G. B. Preston \| title=Representations of inverse semi-groups \| journal=Journal of the London Mathematical Society \| year=1954c \| volume=29 \| pages=411–419 \| doi=10.1112/jlms/s1-29.4.411 }}		*{{cite journal \| author=G. B. Preston \| title=Representations of inverse semi-groups \| journal=Journal of the London Mathematical Society \| year=1954c \| volume=29 \| pages=411–419 \| doi=10.1112/jlms/s1-29.4.411 }}
	*{{cite journal \| author=B. M. Schein \| title=Obituary: Viktor Vladimirovich Vagner (1908–1981) \| journal=Semigroup Forum \| year=1981 \| volume=28 \| pages=189–200 \| doi=10.1007/BF02676643 }}		*{{cite journal \| author=B. M. Schein \| title=Obituary: Viktor Vladimirovich Vagner (1908–1981) \| journal=Semigroup Forum \| year=1981 \| volume=28 \| pages=189–200 \| doi=10.1007/BF02676643 }}
	*{{cite journal \| author=B. M. Schein \| title=Book ~~Review~~: "Inverse Semigroups: The Theory of Partial Symmetries" by Mark V. Lawson \| journal=Semigroup Forum \| year=2002 \| volume=65 \| pages=149–158 \| doi=10.1007/s002330010132 }}		*{{cite journal \| author=B. M. Schein \| title=Book RevieWikipedia: "Inverse Semigroups: The Theory of Partial Symmetries" by Mark V. Lawson \| journal=Semigroup Forum \| year=2002 \| volume=65 \| pages=149–158 \| doi=10.1007/s002330010132 }}
	*{{cite journal \| author=V. V. Wagner \| title=Generalised groups \| journal=[[Proceedings of the USSR Academy of Sciences]] \| year=1952 \| volume=84 \| pages=1119–1122 }} {{ru icon}} English translation: [http://uk.geocities.com/cdhollings/vagner1.pdf]		*{{cite journal \| author=V. V. Wagner \| title=Generalised groups \| journal=[[Proceedings of the USSR Academy of Sciences]] \| year=1952 \| volume=84 \| pages=1119–1122 }} {{ru icon}} English translation: [http://uk.geocities.com/cdhollings/vagner1.pdf]
	*{{cite journal \| author=V. V. Wagner \| title=The theory of generalised heaps and generalised groups \| journal=Matematicheskii Sbornik (N.S.) \| year=1953 \| volume=32(74) \| pages=545–632 }} {{ru icon}}		*{{cite journal \| author=V. V. Wagner \| title=The theory of generalised heaps and generalised groups \| journal=Matematicheskii Sbornik (N.S.) \| year=1953 \| volume=32(74) \| pages=545–632 }} {{ru icon}}

wikademia>Wikademia: moved Inverse semigroup to Archive:Inverse semigroup

2009-04-10T21:22:58Z

moved Inverse semigroup to Archive:Inverse semigroup

← Older revision	Revision as of 21:22, 10 April 2009
(No difference)

wikademia>Wikademia at 05:21, 24 March 2009

2009-03-24T05:21:31Z

← Older revision		Revision as of 05:21, 24 March 2009
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	''y'' in ''S'' in the sense that ''x = xyx'' and ''y = yxy''. Inverse semigroups appear in a range of contexts; for		''y'' in ''S'' in the sense that ''x = xyx'' and ''y = yxy''. Inverse semigroups appear in a range of contexts; for
	example, they can be employed in the study [[partial symmetries]].<ref>Lawson 1998.</ref>		example, they can be employed in the study [[partial symmetries]].<ref>Lawson 1998.</ref>
			{{RightToc}}
	(The convention followed in this article will be that of writing a function on the right of its argument, and		(The convention followed in this article will be that of writing a function on the right of its argument, and
	composing functions from left to right — a convention often observed in semigroup theory.)		composing functions from left to right — a convention often observed in semigroup theory.)

wikademia>Wikademia: 24 revisions

2009-03-21T11:31:04Z

24 revisions

← Older revision	Revision as of 11:31, 21 March 2009
(No difference)

wikademia>Zundark: remove repetitive links + remove see-also to non-existent article

2009-01-23T19:25:48Z

remove repetitive links + remove see-also to non-existent article

← Older revision		Revision as of 19:25, 23 January 2009
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	β; otherwise, the composition αβ is undefined. Under this alternative composition, the collection		β; otherwise, the composition αβ is undefined. Under this alternative composition, the collection
	of all partial one-one transformations of a set forms not an inverse semigroup but an [[inductive groupoid]], in the		of all partial one-one transformations of a set forms not an inverse semigroup but an [[inductive groupoid]], in the
	sense of [[category theory]]. This close connection between inverse semigroups and [[inductive groupoids]] is		sense of [[category theory]]. This close connection between inverse semigroups and inductive groupoids is
	embodied in the ''Ehresmann-Schein-Nambooripad Theorem'', which states that an [[inductive groupoid]] can always be		embodied in the ''Ehresmann-Schein-Nambooripad Theorem'', which states that an inductive groupoid can always be
	constructed from an inverse semigroup, and conversely.<ref>Lawson 1998 : 4.1.8.</ref>		constructed from an inverse semigroup, and conversely.<ref>Lawson 1998 : 4.1.8.</ref>

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	*[[Green's relations]]		*[[Green's relations]]
	*[[Category theory]]		*[[Category theory]]
	*[[Inductive groupoid]]

	[[Category:Abstract algebra]]		[[Category:Abstract algebra]]
	[[Category:Semigroup theory]]		[[Category:Semigroup theory]]

wikademia>Lightbot: Units/dates/other

2009-01-03T09:30:38Z

Units/dates/other

← Older revision		Revision as of 09:30, 3 January 2009
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	== Origins ==		== Origins ==
	Inverse semigroups were introduced independently by [[Viktor Vladimirovich Wagner]]<ref>Since his father was German, Wagner preferred the German transliteration of his name (with a "W", rather than a "V") from Cyrillic - see Schein 1981.</ref> in the [[Soviet Union]] in [[1952]]<ref>First a short announcement in Wagner 1952, then a much more comprehensive exposition in Wagner 1953.</ref>, and by [[Gordon Preston]] in [[Great Britain]] in [[1954]]<ref>Preston 1954a,b,c.</ref>. Both authors arrived at inverse semigroups via the study of partial one-one transformations of a [[Set (mathematics)\|set]]: a [[partial function\|partial transformation]] α of a set ''X'' is a [[Function (mathematics)\|function]] from ''A'' to		Inverse semigroups were introduced independently by [[Viktor Vladimirovich Wagner]]<ref>Since his father was German, Wagner preferred the German transliteration of his name (with a "W", rather than a "V") from Cyrillic - see Schein 1981.</ref> in the [[Soviet Union]] in 1952<ref>First a short announcement in Wagner 1952, then a much more comprehensive exposition in Wagner 1953.</ref>, and by [[Gordon Preston]] in [[Great Britain]] in 1954<ref>Preston 1954a,b,c.</ref>. Both authors arrived at inverse semigroups via the study of partial one-one transformations of a [[Set (mathematics)\|set]]: a [[partial function\|partial transformation]] α of a set ''X'' is a [[Function (mathematics)\|function]] from ''A'' to
	''B'', where ''A'' and ''B'' are subsets of ''X''. Let α and β be partial transformations of a set		''B'', where ''A'' and ''B'' are subsets of ''X''. Let α and β be partial transformations of a set
	''X''; α and β can be composed (from left to right) on the largest [[Domain (mathematics)\|domain]] upon		''X''; α and β can be composed (from left to right) on the largest [[Domain (mathematics)\|domain]] upon

wikademia>CDH: Corrected link to translation of Wagner's paper

2008-10-03T11:35:51Z

Corrected link to translation of Wagner's paper

← Older revision		Revision as of 11:35, 3 October 2008
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	*{{cite journal \| author=B. M. Schein \| title=Obituary: Viktor Vladimirovich Vagner (1908–1981) \| journal=Semigroup Forum \| year=1981 \| volume=28 \| pages=189–200 \| doi=10.1007/BF02676643 }}		*{{cite journal \| author=B. M. Schein \| title=Obituary: Viktor Vladimirovich Vagner (1908–1981) \| journal=Semigroup Forum \| year=1981 \| volume=28 \| pages=189–200 \| doi=10.1007/BF02676643 }}
	*{{cite journal \| author=B. M. Schein \| title=Book Review: "Inverse Semigroups: The Theory of Partial Symmetries" by Mark V. Lawson \| journal=Semigroup Forum \| year=2002 \| volume=65 \| pages=149–158 \| doi=10.1007/s002330010132 }}		*{{cite journal \| author=B. M. Schein \| title=Book Review: "Inverse Semigroups: The Theory of Partial Symmetries" by Mark V. Lawson \| journal=Semigroup Forum \| year=2002 \| volume=65 \| pages=149–158 \| doi=10.1007/s002330010132 }}
	*{{cite journal \| author=V. V. Wagner \| title=Generalised groups \| journal=[[Proceedings of the USSR Academy of Sciences]] \| year=1952 \| volume=84 \| pages=1119–1122 }} {{ru icon}} English translation: [http://~~www-users~~.~~york~~.~~ac.uk~~/~~~cdh500~~/vagner1.pdf]		*{{cite journal \| author=V. V. Wagner \| title=Generalised groups \| journal=[[Proceedings of the USSR Academy of Sciences]] \| year=1952 \| volume=84 \| pages=1119–1122 }} {{ru icon}} English translation: [http://uk.geocities.com/cdhollings/vagner1.pdf]
	*{{cite journal \| author=V. V. Wagner \| title=The theory of generalised heaps and generalised groups \| journal=Matematicheskii Sbornik (N.S.) \| year=1953 \| volume=32(74) \| pages=545–632 }} {{ru icon}}		*{{cite journal \| author=V. V. Wagner \| title=The theory of generalised heaps and generalised groups \| journal=Matematicheskii Sbornik (N.S.) \| year=1953 \| volume=32(74) \| pages=545–632 }} {{ru icon}}

wikademia>Salix alba: fix link to set (mathematics) using AWB

2008-09-20T11:04:08Z

fix link to set (mathematics) using AWB

← Older revision		Revision as of 11:04, 20 September 2008
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	== Origins ==		== Origins ==
	Inverse semigroups were introduced independently by [[Viktor Vladimirovich Wagner]]<ref>Since his father was German, Wagner preferred the German transliteration of his name (with a "W", rather than a "V") from Cyrillic - see Schein 1981.</ref> in the [[Soviet Union]] in [[1952]]<ref>First a short announcement in Wagner 1952, then a much more comprehensive exposition in Wagner 1953.</ref>, and by [[Gordon Preston]] in [[Great Britain]] in [[1954]]<ref>Preston 1954a,b,c.</ref>. Both authors arrived at inverse semigroups via the study of partial one-one transformations of a [[set]]: a [[partial function\|partial transformation]] α of a set ''X'' is a [[Function (mathematics)\|function]] from ''A'' to		Inverse semigroups were introduced independently by [[Viktor Vladimirovich Wagner]]<ref>Since his father was German, Wagner preferred the German transliteration of his name (with a "W", rather than a "V") from Cyrillic - see Schein 1981.</ref> in the [[Soviet Union]] in [[1952]]<ref>First a short announcement in Wagner 1952, then a much more comprehensive exposition in Wagner 1953.</ref>, and by [[Gordon Preston]] in [[Great Britain]] in [[1954]]<ref>Preston 1954a,b,c.</ref>. Both authors arrived at inverse semigroups via the study of partial one-one transformations of a [[Set (mathematics)\|set]]: a [[partial function\|partial transformation]] α of a set ''X'' is a [[Function (mathematics)\|function]] from ''A'' to
	''B'', where ''A'' and ''B'' are subsets of ''X''. Let α and β be partial transformations of a set		''B'', where ''A'' and ''B'' are subsets of ''X''. Let α and β be partial transformations of a set
	''X''; α and β can be composed (from left to right) on the largest [[Domain (mathematics)\|domain]] upon		''X''; α and β can be composed (from left to right) on the largest [[Domain (mathematics)\|domain]] upon

wikademia>Geometry guy: /* Notes */ 2 column

2008-09-14T09:26:52Z

Notes: 2 column

← Older revision		Revision as of 09:26, 14 September 2008
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	== Notes ==		== Notes ==
	~~<references/>~~		{{reflist\|2}}

	== References ==		== References ==

wikademia>Michael Hardy: minus signs, mdahes, and ndashes where appropriate, rather than stubby littlle hyphens

2008-07-17T18:10:09Z

minus signs, mdahes, and ndashes where appropriate, rather than stubby littlle hyphens

Show changes

← Older revision		Revision as of 18:20, 11 April 2009
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	*{{cite journal \| author=G. B. Preston \| title=Representations of inverse semi-groups \| journal=Journal of the London Mathematical Society \| year=1954c \| volume=29 \| pages=411–419 \| doi=10.1112/jlms/s1-29.4.411 }}		*{{cite journal \| author=G. B. Preston \| title=Representations of inverse semi-groups \| journal=Journal of the London Mathematical Society \| year=1954c \| volume=29 \| pages=411–419 \| doi=10.1112/jlms/s1-29.4.411 }}
	*{{cite journal \| author=B. M. Schein \| title=Obituary: Viktor Vladimirovich Vagner (1908–1981) \| journal=Semigroup Forum \| year=1981 \| volume=28 \| pages=189–200 \| doi=10.1007/BF02676643 }}		*{{cite journal \| author=B. M. Schein \| title=Obituary: Viktor Vladimirovich Vagner (1908–1981) \| journal=Semigroup Forum \| year=1981 \| volume=28 \| pages=189–200 \| doi=10.1007/BF02676643 }}
	*{{cite journal \| author=B. M. Schein \| title=Book ~~Review~~: "Inverse Semigroups: The Theory of Partial Symmetries" by Mark V. Lawson \| journal=Semigroup Forum \| year=2002 \| volume=65 \| pages=149–158 \| doi=10.1007/s002330010132 }}		*{{cite journal \| author=B. M. Schein \| title=Book RevieWikipedia: "Inverse Semigroups: The Theory of Partial Symmetries" by Mark V. Lawson \| journal=Semigroup Forum \| year=2002 \| volume=65 \| pages=149–158 \| doi=10.1007/s002330010132 }}
	*{{cite journal \| author=V. V. Wagner \| title=Generalised groups \| journal=[[Proceedings of the USSR Academy of Sciences]] \| year=1952 \| volume=84 \| pages=1119–1122 }} {{ru icon}} English translation: [http://uk.geocities.com/cdhollings/vagner1.pdf]		*{{cite journal \| author=V. V. Wagner \| title=Generalised groups \| journal=[[Proceedings of the USSR Academy of Sciences]] \| year=1952 \| volume=84 \| pages=1119–1122 }} {{ru icon}} English translation: [http://uk.geocities.com/cdhollings/vagner1.pdf]
	*{{cite journal \| author=V. V. Wagner \| title=The theory of generalised heaps and generalised groups \| journal=Matematicheskii Sbornik (N.S.) \| year=1953 \| volume=32(74) \| pages=545–632 }} {{ru icon}}		*{{cite journal \| author=V. V. Wagner \| title=The theory of generalised heaps and generalised groups \| journal=Matematicheskii Sbornik (N.S.) \| year=1953 \| volume=32(74) \| pages=545–632 }} {{ru icon}}

← Older revision		Revision as of 11:35, 3 October 2008
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	*{{cite journal \| author=B. M. Schein \| title=Obituary: Viktor Vladimirovich Vagner (1908–1981) \| journal=Semigroup Forum \| year=1981 \| volume=28 \| pages=189–200 \| doi=10.1007/BF02676643 }}		*{{cite journal \| author=B. M. Schein \| title=Obituary: Viktor Vladimirovich Vagner (1908–1981) \| journal=Semigroup Forum \| year=1981 \| volume=28 \| pages=189–200 \| doi=10.1007/BF02676643 }}
	*{{cite journal \| author=B. M. Schein \| title=Book Review: "Inverse Semigroups: The Theory of Partial Symmetries" by Mark V. Lawson \| journal=Semigroup Forum \| year=2002 \| volume=65 \| pages=149–158 \| doi=10.1007/s002330010132 }}		*{{cite journal \| author=B. M. Schein \| title=Book Review: "Inverse Semigroups: The Theory of Partial Symmetries" by Mark V. Lawson \| journal=Semigroup Forum \| year=2002 \| volume=65 \| pages=149–158 \| doi=10.1007/s002330010132 }}
	*{{cite journal \| author=V. V. Wagner \| title=Generalised groups \| journal=[[Proceedings of the USSR Academy of Sciences]] \| year=1952 \| volume=84 \| pages=1119–1122 }} {{ru icon}} English translation: [http://~~www-users~~.~~york~~.~~ac.uk~~/~~~cdh500~~/vagner1.pdf]		*{{cite journal \| author=V. V. Wagner \| title=Generalised groups \| journal=[[Proceedings of the USSR Academy of Sciences]] \| year=1952 \| volume=84 \| pages=1119–1122 }} {{ru icon}} English translation: [http://uk.geocities.com/cdhollings/vagner1.pdf]
	*{{cite journal \| author=V. V. Wagner \| title=The theory of generalised heaps and generalised groups \| journal=Matematicheskii Sbornik (N.S.) \| year=1953 \| volume=32(74) \| pages=545–632 }} {{ru icon}}		*{{cite journal \| author=V. V. Wagner \| title=The theory of generalised heaps and generalised groups \| journal=Matematicheskii Sbornik (N.S.) \| year=1953 \| volume=32(74) \| pages=545–632 }} {{ru icon}}