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, much like the partitioners of most Catholic churches. 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 a
Attributes | Values |
---|---|
rdfs:label |
|
rdfs:comment |
|
dcterms:subject | |
Wikipage page ID |
|
Wikipage revision ID |
|
Link from a Wikipage to another Wikipage | |
sameAs | |
dbp:wikiPageUsesTemplate | |
has abstract |
|
gold:hypernym | |
prov:wasDerivedFrom | |
page length (characters) of wiki page |
|
foaf:isPrimaryTopicOf | |
is Link from a Wikipage to another Wikipage of | |
is foaf:primaryTopic of |