Results 41 to 50 of about 91 (84)
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Hyperidentities of QZ-algebras
Siberian Mathematical Journal, 1989The symbol \({\mathfrak P}^*_ A\) denotes the algebra \(\) of type \(\) where \(P_ A\) is the set of all operations on A and \((\zeta f)(x_ 1,...,x_ n)=f(x_ 2,...,x_ n,x_ 1)\), \((\tau f)(x_ 1,...,x_ n)=f(x_ 2,x_ 1,x_ 3,...,x_ n)\), \((\Delta f)(x_ 1,...,x_ n)=f(x_ 1,x_ 1,x_ 2,...,x_{n- 1})\), \((f*g)(x_ 1,...,x_{n+m-1})=f(g(x_ 1,..,x_ m),x_{m+1 ...
Mal'tsev, I. A., Schweigert, D.
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Hyperidentities of lattices and semilattices
Algebra Universalis, 1981Following W. Taylor we define a hyperidentity ∈ to be formally the same as an identity (e.g.,F(G(x, y, z), G(x, y, z))=G(x, y, z)). However, a varietyV is said to satisfy a hyperidentity ∈, if whenever the operation symbols of ∈ are replaced by any choice of polynomials (appropriate forV) of the same arity as the corresponding operation symbols of ...
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Separation of clones by means of hyperidentities
Siberian Mathematical Journal, 1994It was shown by \textit{K. Denecke}, \textit{D. Lau}, \textit{R. Pöschel} and \textit{D. Schweigert} [Contrib. Gen. Algebra 7, 97-118 (1991; Zbl 0759.08005)] that, given two nonisomorphic clones \(C\) and \(C'\) of Boolean functions with \(C'\not\cong C\), \(C'\nsubseteq C\), and \(C\nsubseteq C'\), the clone \(C\) can be separated from \(C'\) by ...
Denecke, Klaus-Dieter, Malcev, I. A.
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Hyperidentities in algebras and varieties
Russian Mathematical Surveys, 1998The article consists of 4 sections. Let us list some results. In Section 1 semigroups, groups and multiplicative groups of fields are represented (and characterized) as semigroups and groups of binary functions with hyperidentities, respectively. In Section 2 it is proved that pairs of groups \((G,H)\), where \(H\trianglelefteq G\), can be represented ...
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1995
Let \({\mathbf A}\) be an algebra. An identity in \({\mathbf A}\) is called a hyperidentity in \({\mathbf A}\) if it is satisfied after replacing the operation symbols by terms of the corresponding arity. The paper gives a survey on the theory of hyperidentitites and its connection to clones.
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Let \({\mathbf A}\) be an algebra. An identity in \({\mathbf A}\) is called a hyperidentity in \({\mathbf A}\) if it is satisfied after replacing the operation symbols by terms of the corresponding arity. The paper gives a survey on the theory of hyperidentitites and its connection to clones.
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Hyperidentities for some varieties of semigroups
Algebra Universalis, 1990Hyperidentities and hypervarieties have been defined by Taylor in [4]. A hypervariety is a class of varieties closed under the formation of equivalent, product, reduct and sub-varieties. Hyperidentities are used to define hypervarieties, in the same way that ordinary identities define varieties.
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THE MULTIPLICATIVE GROUP OF A FIELD AND HYPERIDENTITIES
Mathematics of the USSR-Izvestiya, 1990The multiplicative group of a field is characterized. By means of a hyperidentity of distributivity, the groups that can be distinguished as the multiplicative group of a field by the hyperidentity of idempotency are characterized. Bibliography: 21 titles.
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A Generalization of the Artin Theorem
Journal of Contemporary Mathematical Analysis, 2021Yu M Movsisyan
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