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Tensor products of partial algebras.

Miquel Monserrat, Francesc Roselló, Joan Torrens (1992)

Publicacions Matemàtiques

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.

Termal groupoids

Jaroslav Ježek (2002)

Czechoslovak Mathematical Journal

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.

Ternary quasigroups and the modular group

Jonathan D. H. Smith (2008)

Commentationes Mathematicae Universitatis Carolinae

For a positive integer n , the usual definitions of n -quasigroups are rather complicated: either by combinatorial conditions that effectively amount to Latin n -cubes, or by 2 n identities on n + 1 different n -ary operations. In this paper, a more symmetrical approach to the specification of n -quasigroups is considered. In particular, ternary quasigroups arise from actions of the modular group.

Ternary semigroups of morphisms of objects in categories

Antoni Chronowski, Miroslav Novotný (1995)

Archivum Mathematicum

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 𝐑𝐄𝐋 n + 1 and 𝐀𝐋𝐆 n which were studied in [5].

Test elements and the Retract Theorem for monounary algebras

Danica Jakubíková-Studenovská, Jozef Pócs (2007)

Czechoslovak Mathematical Journal

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 𝒜 = ( A , F ) , where each f F is unary and card F > 1 .

The algebra of mode homomorphisms

Kira Adaricheva, Anna Romanowska, Jonathan Smith (2014)

Open Mathematics

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...

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