Ring semigroups whose subsemigroups form a chain |
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Authors: | Greg Oman |
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Institution: | (1) Department of Mathematics, The Ohio State University, 231 W. 18th Ave., Columbus, OH 43210, USA |
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Abstract: | A multiplicative semigroup S is called a ring semigroup if an addition may be defined on S so that (S,+,⋅) is a ring. Such semigroups have been well-studied in the literature (see Bell in Words, Languages and Combinatorics,
pp. 24–31, World Scientific, Singapore, 1994; Jones in Semigroup Forum 47(1):1–6, 1993; Jones and Ligh in Semigroup Forum 17(2):163–173, 1979). In this note, we use Mihăilescu’s Theorem (formerly Catalan’s Conjecture) to characterize the ring semigroups whose subsemigroups
containing 0 form a chain with respect to set inclusion. |
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Keywords: | Ring semigroup Catalan’ s conjecture Quasi-cyclic group Chain semigroup |
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