On covarieties of coalgebras
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 generalized products preserving compactness.
On Levi quasivarieties generated by nilpotent groups.
On locally small based algebraic theories
On n-permutable equivalence relations in regular categories
On quasivarieties of nilpotent Moufang loops. I
In this part the smallest non-abelian quasivarieties for nilpotent Moufang loops are described.
On quasivarieties of nilpotent Moufang loops. II
In this part of the paper we study the quasiidentities of the nilpotent Moufang loops. In particular, we solve the problem of finite basis for quasiidentities in the finitely generated nilpotent Moufang loop.
On quasivarieties of partial algebras, their generation and their subquasivarieties. I
On quasivarieties of partial algebras, their generation and their subquasivarieties II
On reductive and distributive algebras
The paper investigates idempotent, reductive, and distributive groupoids, and more generally -algebras of any type including the structure of such groupoids as reducts. In particular, any such algebra can be built up from algebras with a left zero groupoid operation. It is also shown that any two varieties of left -step reductive -algebras, and of right -step reductive -algebras, are independent for any positive integers and . This gives a structural description of algebras in the join of...
On regular implicit operations
On relational selections for complete theories.
On some correspondences between relational structures and algebras
On some properties a projective model class passes on to the generated axiomatic class.
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 synchronized relatively full embeddings and -universality
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 congruence lattice of stable algebras with definability of compact congruences