International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 3, Pages 487-501
Isomorphisms of semigroups of transformations
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 is a centered operand over a semigroup , the suboperands of containing zero are characterized in terms of -homomorphisms of . Some properties of centered operands over a semigroup with zero are studied.
A -centralizer of a set and the semigroup of transformations of over are introduced, where is a subset of . When , is a faithful and irreducible centered operand over . Theorems concerning the isomorphisms of semigroups of transformations of sets over -centralizers , are obtained, and the following theorem in ring theory is deduced: Let , be the rings of linear transformations of vector spaces not necessarily finite dimensional. Then is an isomorphism of if and only if there exists a semilinear transformation of onto such that for all .