On monoids of injective partial cofinite selfmaps

Oleg Gutik (Author), Dušan Repovš (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 ▫$\mathscr{I}^{\mathrm{cf}}_\lambda$▫.

Keywords

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

Data

Language:	English
Year of publishing:	2015
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	512.536
COBISS:	17538393
ISSN:	0139-9918
Views:	485
Downloads:	339
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	teorija grup;polgrupe;kongruenca;simetrične grupe;poldirektni produkt;
Type (COBISS):	Article
Pages:	str. 981-992
Volume:	ǂVol. ǂ65
Issue:	ǂno. ǂ5
Chronology:	2015
DOI:	http://dx.doi.org/10.1515/ms-2015-0067
ID:	11233709