On some medial semigroups with an associate subgroup |
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Authors: | Mario Petrich |
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Institution: | 1.Bra?,Croatia |
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Abstract: | Let S be a semigroup and s,t∈S. We say that t is an associate of s if s=sts. If S has a maximal subgroup G such that every element s of S has a unique associate in G, say s
∗, we say that G is an associate subgroup of S and consider the mapping s→s
∗ as a unary operation on S. In this way, semigroups with an associate subgroup may be identified with unary semigroups satisfying three simple axioms.
Among them, only those satisfying the identity (st)∗=t
∗
s
∗, called medial, have a structure theorem, due to Blyth and Martins. |
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Keywords: | |
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