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Completely Regular Semigroup Varieties
Synthesis Lectures on Mathematics and StatisticsMario Petrich, Norman R Reilly
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Orders in completely regular semigroups
Mathematika, 2001A classic theorem of semigroup theory is that a semigroup \(S\) has a group of quotients if and only if it is reversible and cancellative. From the perspective of the group, it contains \(S\) as an ``order''. Generalizing from both this situation and from ring theory, a semigroup \(S\) is an order in another semigroup \(Q\) if every element in \(Q ...
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Perfect Completely Regular Semigroups
Mathematische Nachrichten, 1985A congruence \(\sigma\) on a semigroup \(S\) is called perfect if for all \(a,b\in S\) we have \((a\sigma)(b\sigma)=(ab)\sigma\) where \(a\sigma\) denotes the \(\sigma\)-class containing \(a\). If every congruence on \(S\) is perfect, \(S\) is called perfect. In this paper the author characterizes perfect completely regular semigroups.
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Unification Types of Completely Regular Semigroups
Journal of Automated Reasoning, 2002Unification theory is concerned with solving equations in relatively free algebraic structures and has become an important topic in theoretical computer science. The paper characterizes the varieties of completely regular semigroups which contain all semilattices and are of unitary, finitary and infinitary unification type, respectively.
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1995
Abstract It is well known that a group (G, μ) can alternatively be regarded as having three operations, namely the binary operation μ : (a, b) ⟼ab, the unary operation a ⟼a-1, and the 0-ary operation (the constant) 1.
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Abstract It is well known that a group (G, μ) can alternatively be regarded as having three operations, namely the binary operation μ : (a, b) ⟼ab, the unary operation a ⟼a-1, and the 0-ary operation (the constant) 1.
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The Lattice of Varieties of Completely Regular Semigroups
Results in Mathematics, 2005The completely regular semigroups form a variety \(\mathcal{CR}\), when considered as unary semigroups. After a period in which various principal ideals of the lattice \({\mathcal L}(\mathcal{CR})\) were described, \textit{L. Polák} [Semigroup Forum 36, No. 3, 253-284 (1987); ibid. 37, No.
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Semigroup Rings of Completely Regular Semigroups
1990A semigroup S is said to be completely regular if and only if it is covered by its subgroups; that is, if and only if, for each a ∈ S, a ∈ a2 S∩S a2. Groups and bands (semigroups of idempotents) are extreme special cases. In this paper a survey is given of results on the Jacobson radical of the semigroup ring of a completely regular semigroup over a ...
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Bases for certain varieties of completely regular semigroups
Commentationes Mathematicae Universitatis Carolinae, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Correspondences of completely regular semigroups and -isomorphisms of semigroups
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1995A correspondence of a semigroup S is any subsemigroup of S × S, and the set of all correspondences of S, with the operations of composition and involution and the relation of set-theoretic inclusion, forms the bundle of correspondences of S, denoted by (S).
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Congruences on Completely Regular Semigroups
Canadian Journal of Mathematics, 1989There are two subjects in the literature on semigroups which have recently attracted great attention: the class of completely regular semigroups (that is semigroups which are unions of their subgroups) and congruences on regular semigroups. In completely regular semigroups, the most popular subject is that of varieties, even though other aspects of ...
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