ON MONOIDS OF INJECTIVE PARTIAL COFINITE SELFMAPS

被引：1

作者：

Gutik, Oleg ^{[1
]}

Repovs, Dusan ^{[2
,3
]}

机构：

[1] Ivan Franko Natl Univ Lviv, Dept Mech & Math, Univ Ska 1, UA-79000 Lvov, Ukraine

[2] Univ Ljubljana, Fac Educ, Ljubljana 1000, Slovenia

[3] Univ Ljubljana, Fac Math & Phys, Ljubljana 1000, Slovenia

来源：

MATHEMATICA SLOVACA | 2015年 / 65卷 / 05期

关键词：

bicyclic semigroup; semigroup of bijective partial transformations; congruence; symmetric group; group congruence; semidirect product; AUTOMORPHISMS;

D O I：

10.1515/ms-2015-0067

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the semigroup I-lambda(cf) of injective partial cofinite selfmaps of an infinite cardinal.. We show that I-lambda(cf) is a bisimple inverse semigroup and each chain of idempotents in I-lambda(cf) is contained in a bicyclic subsemigroup of I-lambda(cf), we describe the Green relations on I-lambda(cf) and we prove that every non-trivial congruence on I-lambda(cf) is a group congruence. Also, we describe the structure of the quotient semigroup I-lambda(cf)/sigma, where s is the least group congruence on I-lambda(cf). (C) 2015 Mathematical Institute Slovak Academy of Sciences

引用

页码：981 / 992

页数：12

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