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On monoids of injective partial cofinite selfmaps
Gutik, Oleg
(
Author
),
Repovš, Dušan
(
Author
)
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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 nontrivial 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 (dk_c)
Tipology:
1.01  Original Scientific Article
Organization:
PEF  Faculty of Education
Year:
2015
Number of pages:
Str. 981992
Numbering:
Vol. 65, no. 5
UDC:
512.536
ISSN on article:
01399918
DOI:
http://dx.doi.org/10.1515/ms20150067
COBISS.SIID:
17538393
Views:
328
Downloads:
258
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Record is a part of a journal
Title:
Mathematica slovaca
Shortened title:
Math. slovaca
Publisher:
Mathematical Institute of the Slovac Academy of Sciences
ISSN:
01399918
COBISS.SIID:
27357184
Secondary language
Language:
Slovenian
Keywords:
teorija grup
,
polgrupe
,
kongruenca
,
simetrične grupe
,
poldirektni produkt
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