Extensions of semigroups by symmetric inverse semigroups of a bounded\n finite rank

2019/06/19 by Олег Гутік, Gutik, Oleg, Oleksandra Sobol +1
Computer Science · Decision Sciences · Mathematics · #20M18 #20M20 #22A15 #54D30 #54H10 #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1906.08329

openalex publication_date 2019/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the semigroup extension mathscrI_\λⁿ(S) of a semigroup\nS by symmetric inverse semigroups of a bounded finite rank. We describe\nidempotents and regular elements of the semigroups mathscrI_\λⁿ(S)\nand \ mathscrI_\λⁿ(S) show that the semigroup\n mathscrI_\λⁿ(S) (\ mathscrI_\λⁿ(S)) is regular,\northodox, inverse or stable if and only if so is S. Green's relations are\ndescribed on the semigroup mathscrI_\λⁿ(S) for an arbitrary monoid\nS. We introduce the conception of a semigroup with strongly tight ideal\nseries, and proved that for any infinite cardinal \λ and any positive\ninteger n the semigroup mathscrI_\λⁿ(S) has a strongly tight ideal\nseries provides so has S. At the finish we show that for every compact\nHausdorff semitopological monoid (S,\τ_S) there exists a unique its compact\ntopological extension\n\( mathscrI_\λⁿ(S),\τ_ mathscrI^\c\) in the\nclass of Haudorff semitopological semigroups.\n

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