International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 8, Pages 459-466
Adjoint regular rings
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.
Let be a ring. The circle operation is the operation
, for all . This operation
gives rise to a semigroup called the adjoint semigroup
or circle semigroup of . We investigate rings in
which the adjoint semigroup is regular. Examples are given which
illustrate and delimit the theory developed.