is a quasi-variety
-гомоморфизмы колец
TC semigroups and inflations.
Tensor products of partial algebras.
In this paper we introduce the tensor product of partial algebras w.r.t. a quasi-primitive class of partial algebras, and we prove some of its main properties. This construction generalizes the well-known tensor product of total algebras w.r.t. varieties.
Term functions on non-Abelian groups of order
Termal groupoids
We investigate the factor of the groupoid of terms through the largest congruence with a given set among its blocks. The set is supposed to be closed for overterms.
Terms and semiterms
Ternary quasigroups and the modular group
For a positive integer , the usual definitions of -quasigroups are rather complicated: either by combinatorial conditions that effectively amount to Latin -cubes, or by identities on different -ary operations. In this paper, a more symmetrical approach to the specification of -quasigroups is considered. In particular, ternary quasigroups arise from actions of the modular group.
Ternary semigroups of morphisms of objects in categories
In this paper the notion of a ternary semigroup of morphisms of objects in a category is introduced. The connection between an isomorphism of categories and an isomorphism of ternary semigroups of morphisms of suitable objects in these categories is considered. Finally, the results obtained for general categories are applied to the categories and which were studied in [5].
Ternary structures and groupoids
Ternary structures and partial semigroups
Test elements and the Retract Theorem for monounary algebras
The term “Retract Theorem” has been applied in literature in connection with group theory. In the present paper we prove that the Retract Theorem is valid (i) for each finite structure, and (ii) for each monounary algebra. On the other hand, we show that this theorem fails to be valid, in general, for algebras of the form , where each is unary and .
The 0-distributivity in the class of subalgebra lattices of Heyting algebras and closure algebras
The a-congruences on S(X) and the S-equivalences on X.
The algebra of mode homomorphisms
Modes are idempotent and entropic algebras. While the mode structure of sets of submodes has received considerable attention in the past, this paper is devoted to the study of mode structure on sets of mode homomorphisms. Connections between the two constructions are established. A detailed analysis is given for the algebra of homomorphisms from submodes of one mode to submodes of another. In particular, it is shown that such algebras can be decomposed as Płonka sums of more elementary homomorphism...
The algebraic uniqueness of the addition of natural numbers.
The amalgamation basis of the category of compact groups.
The ascending varietal chain of a variety of semigroups.
The automorphism group of unary algebras.
The automorphisms groups of symmetric algebras