Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585315120210701On epimorphisms and structurally regular semigroups23125310118910.52547/cgasa.15.1.231ENAftab HussainShahDepartment of Mathematics of Central University of Kashmir, Ganderbal, India0000-0003-1143-0199Sakeena BanoDepartment of Mathematics Central University of Kashmir, Ganderbal, IndiaShabir AhmadAhangerDepartment of Mathematics Central University of Kashmir, Ganderbal, IndiaWajih AshrafDepartment of Mathematics, Aligarh Muslim University, Aligarh, IndiaJournal Article20210627In this paper we study epimorphisms, dominions and related<br /> properties for some classes of structurally (n,m)-regular semigroups for any<br /> pair (n,m) of positive integers. In Section 2, after a brief introduction of<br /> these semigroups, we prove that the class of structurallly (n,m)-generalized<br /> inverse semigroups is closed under morphic images. We then prove the main<br /> result of this section that the class of structurally (n,m)-generalized inverse<br /> semigroups is saturated and, thus, in the category of all semigroups, epimorphisms<br /> in this class are precisely surjective morphisms. Finally, in the last<br /> section, we prove that the variety of structurally (o, n)-left regular bands is<br /> saturated in the variety of structurally (o, k)-left regular bands for all positive<br /> integers k and n with 1 ≤ k ≤ n.https://cgasa.sbu.ac.ir/article_101189_0013e900e44eab4f80dce782861984eb.pdf