On Closedness of Some Homotypical Varieties of Semigroups

Noor Alam, Aftab Hussain Shah, Sakeena Bano, Sofian Obeidat, Nabawia Shaban Diab, Anas Altaleb and Faranak Farshadifar

Journal of Mathematics, 2024, vol. 2024, 1-16

Abstract: It is well known that every subvariety of the variety of semigroups need not be absolutely closed. Thus, identifying those subvarieties that are closed in themselves or in larger varieties is an interesting open problem in the theory of semigroup dominions. The significance of finding such varieties lies in the fact that, in these varieties, epimorphisms are precisely the surjective morphisms. In this paper, we address this problem and demonstrate that for each n∈N, the varieties of semigroups Vn≔x1x2x3=xj1xinxj2xj3, where i∈1,2,3 and j is any nontrivial permutation of 1,2,3 not fixing 1 when i=2, are closed.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:4402654

DOI: 10.1155/2024/4402654

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