International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 8, Pages 459-466
doi:10.1155/S0161171202109239

Adjoint regular rings

Henry E. Heatherly1 and Ralph P. Tucci2

1Department of Mathematics, University of Louisiana at Lafayette, Lafayette 70504-1010, LA, USA
2Department of Mathematics and Computer Science, Loyola University, New Orleans 70118, LA, USA

Received 10 September 2001

Copyright © 2002 Henry E. Heatherly and Ralph P. Tucci. 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.

Abstract

Let R be a ring. The circle operation is the operation a∘b=a+b−ab, for all a,b∈R. This operation gives rise to a semigroup called the adjoint semigroup or circle semigroup of R. We investigate rings in which the adjoint semigroup is regular. Examples are given which illustrate and delimit the theory developed.