Ring semigroups whose subsemigroups intersect |
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| Authors: | Greg Oman |
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| Institution: | (1) Otterbein College, Department of Mathematics, One Otterbein College, Westerville, OH 43081-2006, USA |
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| Abstract: | A multiplicative semigroup S is said to be a ring semigroup provided there exists an addition + on S such that (S,+,⋅) is a ring. In this note, we characterize the ring semigroups S with the property that every two nonzero subsemigroups intersect. |
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| Keywords: | Ring semigroup Jacobson’ s theorem Nilring Absolutely algebraic field |
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