The spectrum of idempotent varieties of algebras with binary operators based on two variable identities.
N.S. Mendelsohn (1978)
Aequationes mathematicae
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N.S. Mendelsohn (1978)
Aequationes mathematicae
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J. Płonka (1976)
Colloquium Mathematicae
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Ágnes Szendrei (1996)
Mathematica Slovaca
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A. R. Blass, L. Falcao, Č. V. Stanojević (1970)
Matematički Vesnik
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Margalida Mas Grimalt, Joan Torrens, Tomasa Calvo, Marc Carbonell (1999)
Mathware and Soft Computing
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This work is devoted to find and study some possible idempotent operators on a finite chain L. Specially, all idempotent operators on L which are associative, commutative and non-decreasing in each place are characterized. By adding one smoothness condition, all these operators reduce to special combinations of Minimum and Maximum.
J. Płonka (1973)
Colloquium Mathematicae
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Stanley Burris (1971)
Colloquium Mathematicae
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Ivan Chajda (2000)
Discussiones Mathematicae - General Algebra and Applications
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Varieties whose algebras have no idempotent element were characterized by B. Csákány by the property that no proper subalgebra of an algebra of such a variety is a congruence class. We simplify this result for permutable varieties and we give a local version of the theorem for varieties with nullary operations.
Anna B. Romanowska (1999)
Commentationes Mathematicae Universitatis Carolinae
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The paper investigates idempotent, reductive, and distributive groupoids, and more generally -algebras of any type including the structure of such groupoids as reducts. In particular, any such algebra can be built up from algebras with a left zero groupoid operation. It is also shown that any two varieties of left -step reductive -algebras, and of right -step reductive -algebras, are independent for any positive integers and . This gives a structural description of algebras in...
Klaus Denecke, Kazem Mahdavi (2000)
Discussiones Mathematicae - General Algebra and Applications
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In [2] it was proved that all hypersubstitutions of type τ = (2) which are not idempotent and are different from the hypersubstitution whichmaps the binary operation symbol f to the binary term f(y,x) haveinfinite order. In this paper we consider the order of hypersubstitutionswithin given varieties of semigroups. For the theory of hypersubstitution see [3].
Klaus Denecke, Somsak Lekkoksung (2009)
Discussiones Mathematicae - General Algebra and Applications
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The theory of hyperidentities generalizes the equational theory of universal algebras and is applicable in several fields of science, especially in computers sciences (see e.g. [2,1]). The main tool to study hyperidentities is the concept of a hypersubstitution. Hypersubstitutions of many-sorted algebras were studied in [3]. On the basis of hypersubstitutions one defines a pair of closure operators which turns out to be a conjugate pair. The theory of conjugate pairs of additive closure...