The Circle Semigroup of a Ring |
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Authors: | H Heatherly R P Tucci |
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Institution: | (1) DEPARTMENT OF MATHEMATICS, UNIVERSITY OF SOUTHWESTERN LOUISIANA, LAFAYETTE, LA, 70504, U.S.A |
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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.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | |
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