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On the complexity of equational decision problems for finite height complemented and orthocomplemented modular lattices
We study the computational complexity of the satisfiability problem and the complement of the equivalence problem for complemented...
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Existence of Independent Quasi-Equational Bases
We give a sufficient condition for a quasivariety K , weaker than the one found earlier by A. V. Kravchenko, A. M. Nurakunov, and the author, which...
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Vaughan-Lee’s nilpotent loop of size 12 is finitely based
From work of Vaughan-Lee in [
12 ] it follows that if a finite nilpotent loop splits into a direct product of factors of prime power order, then its... -
Equational Theories of Twisted Involution Semigroups
Every twisted involution semigroup with non-finitely based semigroup reduct is shown to be non-finitely based.
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Tropical representations and identities of the stylic monoid
We exhibit a faithful representation of the stylic monoid of every finite rank as a monoid of upper unitriangular matrices over the tropical...
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Equational Noethericity of Metabelian r-Groups
The author had earlier defined the concept of an r -group, generalizing the concept of a rigid (solvable) group. This article proves that every...
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Varieties of Burnside ai-semirings satisfying xn ≈ x
We study the ai-semiring variety defined by the identity x n ≈ x . We show that some subvarieties of this variety are determined by certain properties...
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Equational Closure and Closure with Respect to Enumeration on a Set of Partial Multivalued Logic Functions
It is proven that for any k ⩾ 2, operators of equational closure and closure with respect to enumeration (Π-operator) generate one and the same...
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Finitely based congruence varieties
We show that for a large class of varieties of algebras, the equational theory of the congruence lattices of the members is not finitely based.
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Structure of Quasivariety Lattices. III. Finitely Partitionable Bases
We prove that each quasivariety containing a B-class has continuum many subquasivarieties with finitely partitionable ω -independent quasi-equational...
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Introduction
This monograph studies the lattice of subquasivarieties of a quasivariety. We consider both the properties that these lattices have, and which...
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On the variety generated by generalized subreducts of Tarski’s algebras of relations
In the paper, a basis of identities for the variety generated by the class of groupoids that are generalized subreducts of Tarski’s algebra of...
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Equationally defined classes of semigroups
We apply, in the context of semigroups, the main theorem from the authors’ paper “Algebras defined by equations” (Higgins and Jackson in J Algebra...
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Basis reduction for cryptogroups and orthogroups
The goal of this note is to provide equivalent bases of identities for subvarieties of completely regular semigroups.
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The Quasivariety \( {\mathbf{S}}{\mathbf{P}}(L_{6}) \). II: A Duality Result
We prove that the category of the complete bi-algebraic (0, 1)-lattices belonging to the quasivariety generated by a certain finite lattice with...
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Identities and bases in the sylvester and Baxter monoids
This paper presents new results on the identities satisfied by the sylvester and Baxter monoids. We show how to embed these monoids, of any rank...
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Free Vector Lattices and Free Vector Lattice Algebras
We show how the existence of various free vector lattices and free vector lattice algebras can be derived from a theorem on equational classes in...