Results 261 to 270 of about 6,883 (313)

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.   +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 ...
openaire   +1 more source

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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