JP Journal of Algebra, Number Theory and Applications
Volume 37, Issue 3, Pages 281 - 291
(December 2015) http://dx.doi.org/10.17654/JPANTADec2015_281_291 |
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A NOTE ON *-SIMPLE RINGS
Wafaa Mohammed Fakieh
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Abstract: It is known that if all proper ideals in a non-reduced ring have no zero- divisors, then the ring is simple. In this paper, we use the concept of *-reversible elements and then prove that if a ring with involution is not reduced and all *-proper ideals do not have any *-reversible elements, then R is *-simple. But if R is reduced and all *-proper ideals do not have any *-reversible element, then R is a direct sum of *-simple rings. |
Keywords and phrases: *-reversible rings, *-reversible elements, *-simple rings. |
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