20.500.12556/RUL-111234 On monoids of injective partial cofinite selfmaps 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 ▫$\mathscr{I}^{\mathrm{cf}}_\lambda$▫. mathematics bicyclic semigroup semigroup of bijective partial transformations congruence symmetric group group congruence semidirect product teorija grup polgrupe kongruenca simetrične grupe poldirektni produkt true false true Angleški jezik Slovenski jezik Članek v reviji 2019-09-26 10:24:20 2019-09-26 10:24:21 2022-08-23 03:41:43 0000-00-00 00:00:00 2015 0 0 Str. 981-992 no. 5 Vol. 65 2015 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.536 0139-9918 http://dx.doi.org/10.1515/ms-2015-0067 17538393 27357184 RAZ_Gutik_Oleg_i2015.pdf RAZ_Gutik_Oleg_i2015.pdf 1 744D5C83B6DC72FE2DD4950ECD54EBB0 7da999fdf86d66d0dd70a56df0720c042125f7e5a94afd06e99be469ac23a88b 565aecf4-a1b7-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=123062 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0