On monoids of injective partial cofinite selfmaps

Oleg Gutik (Avtor), Dušan Repovš (Avtor)

Povzetek

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

Ključne besede

teorija grup;polgrupe;kongruenca;simetrične grupe;poldirektni produkt;mathematics;bicyclic semigroup;semigroup of bijective partial transformations;congruence;symmetric group;group congruence;semidirect product;

Podatki

Jezik:	Angleški jezik
Leto izida:	2015
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
UDK:	512.536
COBISS:	17538393
ISSN:	0139-9918
Št. ogledov:	485
Št. prenosov:	339
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Slovenski jezik
Sekundarne ključne besede:	teorija grup;polgrupe;kongruenca;simetrične grupe;poldirektni produkt;
Vrsta dela (COBISS):	Članek v reviji
Strani:	str. 981-992
Letnik:	ǂVol. ǂ65
Zvezek:	ǂno. ǂ5
Čas izdaje:	2015
DOI:	http://dx.doi.org/10.1515/ms-2015-0067
ID:	11233709