Geodesic
σ-Reflexive Semigroups and Rings
Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 185-188

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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. 
Chacrono, M.; Thierrin, G. σ-Reflexive Semigroups and Rings. Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 185-188. doi: 10.4153/CMB-1972-033-3
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     author = {Chacrono, M. and Thierrin, G.},
     title = {\ensuremath{\sigma}-Reflexive {Semigroups} and {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {185--188},
     year = {1972},
     volume = {15},
     number = {2},
     doi = {10.4153/CMB-1972-033-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-033-3/}
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