Abstract
Let R be a ring and define x ○ y = x + y - xy, which yields a monoid (R, ○), called the circle semigroup of R. This paper investigates the relationship between the ring and its circle semigroup. Of particular interest are the cases where the semigroup is simple, 0-simple, cancellative, 0-cancellative, regular, inverse, or the union of groups, or where the ring is simple, regular, or a domain. The idempotents in R coincide with the idempotents in (R, ○) and play an important role in the theory developed.
Similar content being viewed by others
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Heatherly, H., Tucci, R.P. The Circle Semigroup of a Ring. Acta Mathematica Hungarica 90, 231–242 (2001). https://doi.org/10.1023/A:1006706629095
Issue Date:
DOI: https://doi.org/10.1023/A:1006706629095