On monoids of injective partial cofinite selfmaps

Gutik, Oleg (avtor), Repovš, Dušan (avtor)

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 ▫$\mathscr{I}^{\mathrm{cf}}_\lambda$▫.

• Jezik: Angleški jezik
• Ključne besede: mathematics, bicyclic semigroup, semigroup of bijective partial transformations, congruence, symmetric group, group congruence, semidirect product
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2015
• Št. strani: Str. 981-992
• Številčenje: Vol. 65, no. 5
• PID: 20.500.12556/RUL-111234
• UDK: 512.536
• ISSN pri članku: 0139-9918
• DOI: http://dx.doi.org/10.1515/ms-2015-0067
• COBISS.SI-ID: 17538393
• Datum objave v RUL: 26.09.2019

Gradivo je del revije

• Naslov: Mathematica slovaca
• Skrajšan naslov: Math. slovaca
• Založnik: De Gruyter, Slovac Academy of Sciences, Mathematical Institute
• ISSN: 0139-9918
• COBISS.SI-ID: 27357184

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: teorija grup, polgrupe, kongruenca, simetrične grupe, poldirektni produkt