On monoids of injective partial cofinite selfmaps

Gutik, Oleg (author), Repovš, Dušan (author)

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
• Keywords: mathematics, bicyclic semigroup, semigroup of bijective partial transformations, congruence, symmetric group, group congruence, semidirect product
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2015
• Number of pages: Str. 981-992
• Numbering: Vol. 65, no. 5
• PID: 20.500.12556/RUL-111234
• UDC: 512.536
• ISSN on article: 0139-9918
• DOI: http://dx.doi.org/10.1515/ms-2015-0067
• COBISS.SI-ID: 17538393
• Publication date in RUL: 26.09.2019

Record is a part of a journal

• Title: Mathematica slovaca
• Shortened title: Math. slovaca
• Publisher: De Gruyter, Slovac Academy of Sciences, Mathematical Institute
• ISSN: 0139-9918
• COBISS.SI-ID: 27357184

Secondary language

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