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
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.