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- Catholic_semigroup abstract "In mathematics, a catholic semigroup is a semigroup in which no two distinct elements have the same set of inverses. The terminology was introduced by B. M. Schein in a paper published in 1979. Every catholic semigroup either is a regular semigroup or has precisely one element that is not regular. The semigroup of all partial transformations of a set is a catholic semigroup. It follows that every semigroup is embeddable in a catholic semigroup. But the full transformation semigroup on a set is not catholic unless the set is a singleton set. Regular catholic semigroups are both left and right reductive, that is, their representations by inner left and right translations are faithful. A regular semigroup is both catholic and orthodox if and only if the semigroup is an inverse semigroup.".
- Catholic_semigroup wikiPageID "43281071".
- Catholic_semigroup wikiPageLength "1112".
- Catholic_semigroup wikiPageOutDegree "10".
- Catholic_semigroup wikiPageRevisionID "657019616".
- Catholic_semigroup wikiPageWikiLink Category:Semigroup_theory.
- Catholic_semigroup wikiPageWikiLink Inverse_semigroup.
- Catholic_semigroup wikiPageWikiLink Orthodox_semigroup.
- Catholic_semigroup wikiPageWikiLink Regular_semigroup.
- Catholic_semigroup wikiPageWikiLink Semigroup.
- Catholic_semigroup wikiPageWikiLink Singleton_(mathematics).
- Catholic_semigroup wikiPageWikiLink Special_classes_of_semigroups.
- Catholic_semigroup wikiPageWikiLink Transformation_(function).
- Catholic_semigroup wikiPageWikiLink Transformation_semigroup.
- Catholic_semigroup wikiPageWikiLinkText "Catholic semigroup".
- Catholic_semigroup wikiPageUsesTemplate Template:Reflist.
- Catholic_semigroup subject Category:Semigroup_theory.
- Catholic_semigroup hypernym Semigroup.
- Catholic_semigroup comment "In mathematics, a catholic semigroup is a semigroup in which no two distinct elements have the same set of inverses. The terminology was introduced by B. M. Schein in a paper published in 1979. Every catholic semigroup either is a regular semigroup or has precisely one element that is not regular. The semigroup of all partial transformations of a set is a catholic semigroup. It follows that every semigroup is embeddable in a catholic semigroup.".
- Catholic_semigroup label "Catholic semigroup".
- Catholic_semigroup sameAs Q18344524.
- Catholic_semigroup sameAs m.0114lpcf.
- Catholic_semigroup sameAs Q18344524.
- Catholic_semigroup wasDerivedFrom Catholic_semigroup?oldid=657019616.
- Catholic_semigroup isPrimaryTopicOf Catholic_semigroup.