On monoids of injective partial cofinite selfmaps
Gutik, Oleg (Author), Repovš, Dušan (Author)

Abstract
We study the semigroup ▫$\mathscr{I}^{\mathrm{cf}}_\lambda$▫ of injective partial cofinite selfmaps of an infinite cardinal ▫$\lambda$▫. We show that ▫$\mathscr{I}^{\mathrm{cf}}_\lambda$▫ is a bisimple inverse semigroup and each chain of idempotents in ▫$\mathscr{I}^{\mathrm{cf}}_\lambda$▫ is contained in a bicyclic subsemigroup of ▫$\mathscr{I}^{\mathrm{cf}}_\lambda$▫, we describe the Green relations on ▫$\mathscr{I}^{\mathrm{cf}}_\lambda$▫ and we prove that every non-trivial congruence on ▫$\mathscr{I}^{\mathrm{cf}}_\lambda$▫ is a group congruence. Also, we describe the structure of the quotient semigroup ▫$\mathscr{I}^{\mathrm{cf}}_\lambda/\sigma$▫, where ▫$\sigma$▫ is the least group congruence on ▫$\mathscr{I}^{\mathrm{cf}}_\lambda$▫.

Language: English mathematics, bicyclic semigroup, semigroup of bijective partial transformations, congruence, symmetric group, group congruence, semidirect product Article (dk_c) 1.01 - Original Scientific Article PEF - Faculty of Education 2015 Str. 981-992 Vol. 65, no. 5 512.536 0139-9918 http://dx.doi.org/10.1515/ms-2015-0067 17538393 328 258 (0 votes) Voting is allowed only to logged in users. AddThis uses cookies that require your consent. Edit consent...

## Record is a part of a journal

Title: Mathematica slovaca Math. slovaca Mathematical Institute of the Slovac Academy of Sciences 0139-9918 27357184

## Secondary language

Language: Slovenian teorija grup, polgrupe, kongruenca, simetrične grupe, poldirektni produkt