Homomorphisms of unary algebras and of their expansions
How to make many-sorted algebras one-sorted
HSP subcategories of Eilenberg-Moore algebras.
Implicit operations on the categories of universal algebras.
Initial models and Horn clause axiomatizability.
Introduction to coalgebra.
Lattice valued algebras.
In this paper we propose a general approach to the theory of fuzzy algebras, while the early existing papers deal with a particular type of fuzzy structures as fuzzy groups, fuzzy ideals, fuzzy vector spaces and so on.
Limit preserving full embeddings.
Minimal algebras and category equivalences
Morita equivalence of algebraic theories
-permutable locally finitely presentable categories.
On exponentiation on n-ary hyperalgebras
For n-ary hyperalgebras we study a binary operation of exponentiation which to a given pair of n-ary hyperalgebras assigns their power, i.e., an n-ary hyperalgebra carried by the corresponding set of homomorphisms. We give sufficient conditions for the existence of such a power and for a decent behaviour of the exponentiation. As a consequence of our investigations we discover a cartesian closed subcategory of the category of n-ary hyperalgebras and homomorphisms between them.
On locally small based algebraic theories
On n-permutable equivalence relations in regular categories
On some correspondences between relational structures and algebras
On some ternary operations in knot theory
We introduce a way to color the regions of a classical knot diagram using ternary operations, so that the number of colorings is a knot invariant. By choosing appropriate substitutions in the algebras that we assign to diagrams, we obtain the relations from the knot group, and from the core group. Using the ternary operator approach, we generalize the Dehn presentation of the knot group to extra loops, and a similar presentation for the core group to the variety of Moufang loops.
On the characterisation of Mal'tsev and Jónsson-Tarski algebras
There are very strong parallels between the properties of Mal'tsev and Jónsson-Tarski algebras, for example in the good behaviour of centrality and in the factorization of direct products. Moreover, the two classes between them include the majority of algebras that actually arise 'in nature'. As a contribution to the research programme building a unified theory capable of covering the two classes, along with other instances of good centrality and factorization, the paper presents a common framework...
On the characterization of Jonsson-Tarski and of subtractive varieties
On the failure of Birkhoff's theorem for locally small based equational categories of algebras
On the structure of equationally complete varieties. I