International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 3, Pages 487-501

Isomorphisms of semigroups of transformations

A. Sita Rama Murti

Department of Mathematics, Andhra University, Waltair, 530 003, India

Received 24 July 1980; Revised 17 April 1981

Copyright © 1983 A. Sita Rama Murti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


If M is a centered operand over a semigroup S, the suboperands of M containing zero are characterized in terms of S-homomorphisms of M. Some properties of centered operands over a semigroup with zero are studied.

A Δ-centralizer C of a set M and the semigroup S(C,Δ) of transformations of M over C are introduced, where Δ is a subset of M. When Δ=M, M is a faithful and irreducible centered operand over S(C,Δ). Theorems concerning the isomorphisms of semigroups of transformations of sets Mi over Δi-centralizers Ci, i=1,2 are obtained, and the following theorem in ring theory is deduced: Let Li, i=1,2 be the rings of linear transformations of vector spaces (Mi,Di) not necessarily finite dimensional. Then f is an isomorphism of L1L2 if and only if there exists a 11 semilinear transformation h of M1 onto M2 such that fT=hTh1 for all TL1.