The class of algebras in which weak independence is equivalent to direct sums independence
The Countable Chain Condition and Free Algebras.
The dimension of a variety
Derived varieties were invented by P. Cohn in [4]. Derived varieties of a given type were invented by the authors in [10]. In the paper we deal with the derived variety of a given variety, by a fixed hypersubstitution σ. We introduce the notion of the dimension of a variety as the cardinality κ of the set of all proper derived varieties of V included in V. We examine dimensions of some varieties in the lattice of all varieties of a given type τ. Dimensions of varieties of lattices and all subvarieties...
The existence of upper semicomplements in lattices of primitive classes
The finiteness of a base of indentities for fiveelement monoids
The hereditary pure monoids.
The number of minimal varieties of idempotent groupoids
The observational predicate calculus and complexity of computations (Preliminary communication)
The semigroup of varieties of weakly associative lattice groups
The spectrum of idempotent varieties of algebras with binary operators based on two variable identities. (Short Communication).
The spectrum of idempotent varieties of algebras with binary operators based on two variable identities.
The strong amalgamation property
The variety covering the variety of all modular lattices.
The weak hereditary class of a variety
We study the weak hereditary class of all weak subalgebras of algebras in a total variety . We establish an algebraic characterization, in the sense of Birkhoff’s HSP theorem, and a syntactical characterization of these classes. We also consider the problem of when such a weak hereditary class is weak equational.
Three Mal'cev Type Theorems and their Application
T-Varieties and Clones of T-terms
The aim of this paper is to describe how varieties of algebras of type τ can be classified by using the form of the terms which build the (defining) identities of the variety. There are several possibilities to do so. In [3], [19], [15] normal identities were considered, i.e. identities which have the form x ≈ x or s ≈ t, where s and t contain at least one operation symbol. This was generalized in [14] to k-normal identities and in [4] to P-compatible identities. More generally, we select a subset...