Adjoint regular rings
Henry E. Heatherly, Ralph P. Tucci · International Journal of Mathematics and Mathematical Sciences · 2002
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.