Results 231 to 240 of about 29,813 (281)

Identities and Quasi-Identities of Pointed Algebras

Siberian Mathematical Journal, 2022
It is proved that if a finite algebra \(\mathbf A\) belongs to a certain variety (quasivariety) then the algebra obtained from \(\mathbf A\) by adding finitely many constant operations admits a finite basis of identities (quasi-identities). Applications of these results and examples are presented.
Basheyeva, A. O., Mustafa, M., Nurakunov, A. M.   +2 more
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Quasi-identities and quasi-verbal subalgebras

Mathematical Notes, 2000
The author studies classes \(\mathcal L\) of universal algebras with a constant term \(c(x)= c(y)\) for all elements \(x,y\) and \( f(c(x),\dots,c(x))= c(x) = c \) for every basic operation \(f\). Given quasivarieties \(\mathcal {U, V}\), \({\mathcal U}*_{\mathcal L} {\mathcal V}\) is the class of all algebras \( A \in \mathcal L\) such that the ...
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Quasi-identities of finite nilpotent groups

Algebra Universalis, 1995
The main theorem of this paper claims the existence of a quasi-identity \(\Phi\) which is true in the free nilpotent class 2 group \(F_2 ({\mathcal N}_2)\) of rank 2, but false in any non-abelian group with no subgroup isomorphic to \(F_2 ({\mathcal N}_2)\), thus giving a negative answer to the question as to whether the quasivariety of torsion-free ...
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Quasi-identities of certain finite algebras

Mathematical Notes of the Academy of Sciences of the USSR, 1977
In this note an example of a finite lattice not having a finite basis of quasiidentities and an analogous example for algebras of the type are indicated.
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Quasi-identities of torsion-free 2-generated groups

Siberian Mathematical Journal, 1995
We prove that the set of \(Q\)-theories of torsion-free 2-generator groups with axiomatic rank \(n\) is of the power of the continuum for every natural number \(n\), \(n \geq 2\).
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Quasi-Identities of Congruence-Distributive Quasivarieties of Algebras

Siberian Mathematical Journal, 2001
Theorem 1. Let \(R\) be a congruence-distributive quasivariety of algebras of finite signature whose class of finitely subdirect \(R\)-indecomposable algebras is finitely axiomatizable. Then there exists a finite number \(n\) (depending on \(R\)) such that, if the congruence lattice of the \(R\)-free algebra of rank \(n\) has at most countable width or
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On quasi-identities of finite nilpotent algebras

Algebra Universalis, 1996
The author proves the conjecture of \textit{V. A. Gorbunov}: ``If a finite algebra \(G\) in a congruence modular variety \(\mathcal V\) has a nilpotent nonabelian subalgebra \(H,\) then the quasivariety generated by \(G\) is not finitely based'' for quasirings, introduced by \textit{A. I. Mal'tsev} in 1953.
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Studying semigroups of mappings using quasi-identities

Semigroup Forum, 2001
A \(pq\)-variety \(V\) is a class of finite semigroups closed under the formation of subsemigroups and finitary direct products; (equivalently \(V\) is defined by a set of quasi-identities, that is identities that are formal consequences of a list of other identities. For example, left cancellativity: \((xy=xz\to y=z)\)).
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On quasi-identities of relation algebras with diophantine operations

Siberian Mathematical Journal, 1997
Let \(\operatorname{Rel}(U)\) denote the set of all binary relations defined on a set \(U\). Consider the set of operations \(F_{\varphi}(r_{1}, \ldots, r_{n}) = (x, y)\), where \(\varphi(x, y, r_{1}, \ldots, r_{n})\) is valid in \(U\) on elements \(x, y\) and relations \(r_{1}, \ldots, r_{n}\). A set of relations \(\Phi \subseteq \operatorname{Rel}(U)\
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