σ-Reflexive Semigroups and Rings
1972 ◽
Vol 15
(2)
◽
pp. 185-188
◽
We shall call a semigroup S a σ-reflexive semigroup if any subsemigroup H in S is reflexive (i.e. for all a, b ∈ S, ab ∈ H implies ba∊H ([2], [5]). It can be verified that any group G is a σ-reflexive semigroup if and only if any subgroup of G is normal. In this paper, we characterize subdirectly irreducible o-reflexive semigroups. We derive the following commutativity result: any generalized commutative ring R ([1]) in which the integers n=n(x, y) in the equation (xy)n = (yx)m can be taken equal to 1 for all x, y ∈ R must be a commutative ring.
2019 ◽
Vol 56
(2)
◽
pp. 252-259
2013 ◽
Vol 42
(4)
◽
pp. 1582-1593
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2014 ◽
Vol 14
(01)
◽
pp. 1550008
◽
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