On Closedness of Some Homotypical Varieties of Semigroups
Noor Alam, Aftab Hussain Shah, Sakeena Bano, Sofian Talal Obeidat, Nabawia Shaban Diab, Anas Altaleb · Journal of Mathematics · 2024
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 , the varieties of semigroups , where i ∈ {1, 2, 3} and j is any nontrivial permutation of {1, 2, 3} not fixing 1 when i = 2, are closed.