On epimorphisms and structurally regular semigroups

Document Type : Research Paper


1 Department of Mathematics of Central University of Kashmir, Ganderbal, India

2 Department of Mathematics Central University of Kashmir, Ganderbal, India

3 Department of Mathematics, Aligarh Muslim University, Aligarh, India


In this paper we study epimorphisms, dominions and related
properties for some classes of structurally (n,m)-regular semigroups for any
pair (n,m) of positive integers. In Section 2, after a brief introduction of
these semigroups, we prove that the class of structurallly (n,m)-generalized
inverse semigroups is closed under morphic images. We then prove the main
result of this section that the class of structurally (n,m)-generalized inverse
semigroups is saturated and, thus, in the category of all semigroups, epimorphisms
in this class are precisely surjective morphisms. Finally, in the last
section, we prove that the variety of structurally (o, n)-left regular bands is
saturated in the variety of structurally (o, k)-left regular bands for all positive
integers k and n with 1 ≤ k ≤ n.


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