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Semigroup Forum, 1975 Some of the next articles are maybe not open access.
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Some relations on completely regular semigroups
Semigroup Forum, 2009Two relations \(Y\) and \(\xi\) on completely regular semigroups \(S\) are studied in connection with the least Clifford congruence \(\nu\) [described by \textit{P. R. Jones}, Semigroup Forum 27, 390-392 (1983; Zbl 0537.20036)]. For \(Y\), defined by: \(aYb\) iff \(V(a)=V(b)\) (where \(V(a)\) denotes the set of all generalized inverses of \(a\in S ...
Zhang, Jiangang, Shen, Ran
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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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New operators for varieties of completely regular semigroups
Semigroup Forum, 2015In a series of articles, starting with [J. Aust. Math. Soc. 83, No. 1, 87-104 (2007; Zbl 1142.20035)], the author has investigated the decomposition of the lattice of varieties of completely regular semigroups induced by intersecting with the variety \(\mathbf B\) of bands.
Mariio Petrich, Petrich Mario
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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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