On semigroups admitting ring structure |
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Authors: | Ryszard Mazurek |
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Institution: | 1.Faculty of Computer Science,Bialystok University of Technology,Bia?ystok,Poland |
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Abstract: | A right-chain semigroup is a semigroup whose right ideals are totally ordered by set inclusion. The main result of this paper
says that if S is a right-chain semigroup admitting a ring structure, then either S is a null semigroup with two elements or sS=S for some s∈S. Using this we give an elementary proof of Oman’s characterization of semigroups admitting a ring structure whose subsemigroups
(containing zero) form a chain. We also apply this result, along with two other results proved in this paper, to show that
no nontrivial multiplicative bounded interval semigroup on the real line ℝ admits a ring structure, obtaining the main results
of Kemprasit et al. (ScienceAsia 36: 85–88, 2010). |
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Keywords: | |
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