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Infinite idempotent quasi-affine algebras need not be hereditarily absorption free
It is known that for finite algebras, solvable implies hereditarily absorption free. We present an example which shows that this implication does not...
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Categorical equivalence and the Ramsey property for finite powers of a primal algebra
In this paper, we investigate the best known and most important example of a categorical equivalence in algebra, that between the variety of boolean...
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On Exponentiable Morphisms in Classical Algebra
We study exponentiability of homomorphisms in varieties of universal algebras close to classical ones. After describing an “almost folklore” general...
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Kleene algebras with implication
Inspired by an old construction due to J. Kalman that relates distributive lattices and centered Kleene algebras, in this paper we study an...
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Loosely-abelian algebras
Abelianity has two different meanings in universal algebra. On the one hand, the term “abelian” is used interchangeably with “commutative” whilst on...
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Menger algebras of n-place interior operations
Algebraic properties of n -place interior operations on a fixed set are described. Conditions under which a Menger algebra of rank n can be...
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Varieties generated by modes of submodes
In a natural way, we can “lift” any operation defined on a set A to an operation on the set of all non-empty subsets of A and obtain from any algebra...
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On some congruences of power algebras
In a natural way we can “lift” any operation defined on a set A to an operation on the set of all non-empty subsets of A and obtain from any algebra (
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Commutative medial ternary groupoids
The paper studies the class of commutative medial ternary groupoids. A construction of ternary semiterms is given and it is proved that the...
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Freeoids: a semi-abstract view on endomorphism monoids of relatively free algebras
A freeoid over a (normally, infinite) set of variables X is defined to be a pair ( W , E ), where W is a superset of X , and E is a submonoid of W ...
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Small clones and the projection property
In 1986, the second author classified the minimal clones on a finite universe into five types. We extend this classification to infinite universes...
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Homomorphisms of direct powers of algebras
We give an example of n-coconnected algebra that is not ( n +1)-coconnected, for any n ≥ 2.
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Minimal clones—a minicourse
This paper provides an elementary introduction to minimal clones, as well as a survey of recent trends and results.
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A characterization of k-normal varieties
Let v be a valuation of terms of type τ, assigning to each term t of type τ a value v(t) ≥ 0. Let k ≥ 1 be a natural number. An identity
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Homomorphisms of algebras
A construction of all homomorphisms of an algebra with a finite number of operations into an algebra of the same type is presented that consists in...
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Minimal clones generated by majority operations
The minimal majority functions of the four-element set are determined.