Displaying similar documents to “The spectrum of idempotent varieties of algebras with binary operators based on two variable identities. (Short Communication).”

Idempotent operators on a finite chain.

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.

Modyfications of Csákány's Theorem

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.

On reductive and distributive algebras

Anna B. Romanowska (1999)

Commentationes Mathematicae Universitatis Carolinae

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The paper investigates idempotent, reductive, and distributive groupoids, and more generally Ω -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 k -step reductive Ω -algebras, and of right n -step reductive Ω -algebras, are independent for any positive integers k and n . This gives a structural description of algebras in...

The order of normalform hypersubstitutions of type (2)

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].

Hyperidentities in many-sorted algebras

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...