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

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. 981-992
Numbering:Vol. 65, no. 5
UDC:512.536
ISSN on article:0139-9918
DOI:http://dx.doi.org/10.1515/ms-2015-0067 This link opens in a new window
COBISS.SI-ID:17538393 This link opens in a new window
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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:0139-9918
COBISS.SI-ID:27357184 This link opens in a new window

Secondary language

Language:Slovenian
Keywords:teorija grup, polgrupe, kongruenca, simetrične grupe, poldirektni produkt

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