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Inverse semigroups which are separated over a subsemigroup


Author: D. B. McAlister
Journal: Trans. Amer. Math. Soc. 182 (1973), 85-117
MSC: Primary 20M10
DOI: https://doi.org/10.1090/S0002-9947-1973-0327952-0
MathSciNet review: 0327952
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Abstract: An inverse semigroup T is separated over a subsemigroup S if T is generated, as an inverse semigroup, by S and for each $ a,b,\epsilon S$ there exists $ x\;\epsilon \;Sa \cap Sb$ such that $ {a^{ - 1}}a{b^{ - 1}}b = {x^{ - 1}}x$ and dually for right ideals. For example, if T is generated as an inverse semigroup by a semigroup S whose principal left and right ideals form chains under inclusion, then T is separated over S. In this paper we investigate the structure of inverse semigroups T which are separated over subsemigroups S.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0327952-0
Keywords: Inverse semigroup, shift representation, free inverse semigroup, naturally quasisemilatticed semigroup, fundamental inverse semigroup, inverse semigroup of (strong) quotients
Article copyright: © Copyright 1973 American Mathematical Society

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