Publication
Regular centralizers of idempotent transformations
| dc.contributor.author | André, Jorge | |
| dc.contributor.author | Araújo, João | |
| dc.contributor.author | Konieczny, Janusz | |
| dc.date.accessioned | 2011-12-19T11:57:22Z | |
| dc.date.available | 2011-12-19T11:57:22Z | |
| dc.date.issued | 2011 | |
| dc.description.abstract | Denote by T(X) the semigroup of full transformations on a set X. For ε∈T(X), the centralizer of ε is a subsemigroup of T(X) defined by C(ε)={α∈T(X):αε=εα}. It is well known that C(id X )=T(X) is a regular semigroup. By a theorem proved by J.M. Howie in 1966, we know that if X is finite, then the subsemigroup generated by the idempotents of C(id X ) contains all non-invertible transformations in C(id X ). This paper generalizes this result to C(ε), an arbitrary regular centralizer of an idempotent transformation ε∈T(X), by describing the subsemigroup generated by the idempotents of C(ε). As a corollary we obtain that the subsemigroup generated by the idempotents of a regular C(ε) contains all non-invertible transformations in C(ε) if and only if ε is the identity or a constant transformation. | por |
| dc.identifier.citation | André, Jorge; Araújo, João; Konieczny, Janusz - Regular centralizers of idempotent transformations. "Semigroup Forum" [Em linha]. ISSN 0037-1912 (Print) 1432-2137 (Online). Vol. 82, nº 2 (Apr. 2011), p. 307-318 | por |
| dc.identifier.other | DOI 10.1007/s00233-010-9274-6 | |
| dc.identifier.uri | http://hdl.handle.net/10400.2/2001 | |
| dc.language.iso | eng | por |
| dc.peerreviewed | yes | por |
| dc.publisher | Springer Verlag | por |
| dc.relation.publisherversion | http://www.springerlink.com/content/c118371784352531/ | por |
| dc.subject | Idempotent transformations | por |
| dc.subject | Regular centralizers | por |
| dc.subject | Generators | por |
| dc.title | Regular centralizers of idempotent transformations | por |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 318 | por |
| oaire.citation.issue | 82 | por |
| oaire.citation.startPage | 307 | por |
| oaire.citation.title | Semigroup Forum | por |
| person.familyName | Ribeiro Soares Gonçalves de Araújo | |
| person.givenName | João Jorge | |
| person.identifier.ciencia-id | EC1F-273A-9F24 | |
| person.identifier.orcid | 0000-0001-6655-2172 | |
| rcaap.rights | openAccess | por |
| rcaap.type | article | por |
| relation.isAuthorOfPublication | 1f7b349c-3251-480d-a3ac-e3cb4ef44f22 | |
| relation.isAuthorOfPublication.latestForDiscovery | 1f7b349c-3251-480d-a3ac-e3cb4ef44f22 |