A relation for general and inverse semigroups |
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Authors: | M Petrich |
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Institution: | (1) Uz Garmu, 21420 Bol Bra, Croatia |
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Abstract: | The relation in the title is S defined by on an arbitrary semigroup. We investigate antisymmetry of S by means of a (minimal) family whose members can not appear as subsemigroups. Transitivity of S is characterized similarly by means of the family and homomorphic images of a certain semigroup. We study the transfer of certain properties of a monoid T and the Bruck semigroup B(T,) over T. The paper concludes with a consideration of certain properties of the relation S on inverse semigroups. |
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Keywords: | relation transitivity quasi-separative semigroup natural partial order Bruck semigroup over a monoid antisymmetry inverse semigroup subsemigroup |
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