Arbitrary vs. regular semigroups
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The notion of regularity for semigroups is studied in this article, and it is shown that an unambiguous semigroup can be embedded in a regular semigroup with the same subgroups and the same ideal structure.About:
This article is published in Journal of Pure and Applied Algebra.The article was published on 1984-10-01 and is currently open access. It has received 21 citations till now. The article focuses on the topics: Regular semigroup & Bicyclic semigroup.read more
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Journal ArticleDOI
Almost finite expansions of arbitrary semigroups
TL;DR: In this paper, the authors describe algebraic techniques that enable them to apply methods of finite semigroup theory to arbitrary infinite semigroups and their morphisms, and to study languages and automata that are not finite-state.
Journal ArticleDOI
Iteration of expansions — unambiguous semigroups
TL;DR: In this article, a new expansion for global semigroup theory is developed, which is invariant under application of the old two expansions and thus has the properties of both (e.g., one obtains -+ with, and so -+ has unambiguous L-and R-order).
Journal ArticleDOI
The Structure of 0- E -unitary inverse semigroups I: the monoid case
TL;DR: In this article, the McAlister structure theory was generalized to O-E-unitary inverse semigroups with a pure prehomomorphism to a primitive inverse semigroup.
Journal ArticleDOI
Profinite semigroups, varieties, expansions and the structure of relatively free profinite semigroups
John Rhodes,Benjamin Steinberg +1 more
TL;DR: The structure of the minimal ideal of relatively free profinite semigroups is studied showing, in particular, that the minimal Ideal of the free Profinite semigroup on a finite set with more than two generators is not a relatively freeProfinite completely simple semigroup, as well as some generalizations to related pseudovarieties.
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Compactable semilattices
TL;DR: The class of 0-disjunctive semilattices, important in the theory of congruence-free inverse semigroups, plays a distinguished role in this theory as mentioned in this paper.
References
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Book
The algebraic theory of semigroups
A. H. Clifford,G. B. Preston +1 more
TL;DR: A survey of the structure and representation theory of semi groups is given in this article, along with an extended treatment of the more important recent developments of Semi Group Structure and Representation.
Journal ArticleDOI
Almost finite expansions of arbitrary semigroups
TL;DR: In this paper, the authors describe algebraic techniques that enable them to apply methods of finite semigroup theory to arbitrary infinite semigroups and their morphisms, and to study languages and automata that are not finite-state.
Journal ArticleDOI
Iteration of expansions — unambiguous semigroups
TL;DR: In this article, a new expansion for global semigroup theory is developed, which is invariant under application of the old two expansions and thus has the properties of both (e.g., one obtains -+ with, and so -+ has unambiguous L-and R-order).