The Chinese remainder theorem and sheaf representations
The class of algebras in which weak independence is equivalent to direct sums independence
The colimits in the generalized algebraic categories
The computability potential scale of all finite algebras.
The concept of structural regularity.
The congruence extension property for algebraic semigroups.
The congruence lattice of implication algebras.
The Countable Chain Condition and Free Algebras.
The Csákány theory of regularity for finite algebras
The degrees of regularity in varieties
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 dual of the category of generalized trees.
The egg-box property of congruences
The epis of the category of ordered algebras and -continuous homomorphisms
The exocenter and type decomposition of a generalized pseudoeffect algebra
We extend the notion of the exocenter of a generalized effect algebra (GEA) to a generalized pseudoeffect algebra (GPEA) and show that elements of the exocenter are in one-to-one correspondence with direct decompositions of the GPEA; thus the exocenter is a generalization of the center of a pseudoeffect algebra (PEA). The exocenter forms a boolean algebra and the central elements of the GPEA correspond to elements of a sublattice of the exocenter which forms a generalized boolean algebra. We extend...
The Galois correspondence between subvariety lattices and monoids of hpersubstitutions
Denecke and Reichel have described a method of studying the lattice of all varieties of a given type by using monoids of hypersubstitutions. In this paper we develop a Galois correspondence between monoids of hypersubstitutions of a given type and lattices of subvarieties of a given variety of that type. We then apply the results obtained to the lattice of varieties of bands (idempotent semigroups), and study the complete sublattices of this lattice obtained through the Galois correspondence.
The ideal structure of simple ternary algebras
The join of equational theories
The lattice of subautomata of an automaton: A survey.
The lattice of varieties of fibered automata
The class of all fibered automata is a variety of two-sorted algebras. This paper provides a full description of the lattice of varieties of fibred automata.