Quelques applications des catégories à involution aux algèbres universelles
Quotient algebraic structures on the set of fuzzy numbers
A. M. Bica has constructed in [6] two isomorphic Abelian groups, defined on quotient sets of the set of those unimodal fuzzy numbers which have strictly monotone and continuous sides. In this paper, we extend the results of above mentioned paper, to a larger class of fuzzy numbers, by adding the flat fuzzy numbers. Furthermore, we add the topological structure and we characterize the constructed quotient groups, by using the set of the continuous functions with bounded variation, defined on .
Quotients and homomorphisms of relational systems
Relational systems containing one binary relation are investigated. Quotient relational systems are introduced and some of their properties are characterized. Moreover, homomorphisms, strong mappings and cone preserving mappings are introduced and the interplay between these notions is considered. Finally, the connection between directed relational systems and corresponding groupoids is investigated.
-systems of unary algebras. I: On maximal and greatest -classes of the direct product of unary algebras
-systems of unary algebras. II: Maximal and minimal subalgebras of the direct products of unary algebras
Radical decompositions of semiheaps
Semiheaps are ternary generalisations of involuted semigroups. The first kind of semiheaps studied were heaps, which correspond closely to groups. We apply the radical theory of varieties of idempotent algebras to varieties of idempotent semiheaps. The class of heaps is shown to be a radical class, as are two larger classes having no involuted semigroup counterparts. Radical decompositions of various classes of idempotent semiheaps are given. The results are applied to involuted I-semigroups, leading...
Random seminormed spaces
Range sets and partition sets in connection with congruences and algebraic invariants.
Rectangular groupoids
Reduced dimension of primitive classes of universal algebras
Rees ideal algebras
We describe algebras and varieties for which every ideal is a kernel of a one-block congruence.
Refinement Monoids, Vaught Monoids, and Boolean Algebras.
Reflexive and antisymmetric relations and their systems
Regular elements and Green's relations in Menger algebras of terms
Defining an (n+1)-ary superposition operation on the set of all n-ary terms of type τ, one obtains an algebra of type (n+1,0,...,0). The algebra n-clone τ is free in the variety of all Menger algebras ([9]). Using the operation there are different possibilities to define binary associative operations on the set and on the cartesian power . In this paper we study idempotent and regular elements as well as Green’s relations in semigroups of terms with these binary associative operations...
Regular elements of the semigroup of all binary relations.
Regular lattices
Regularity and permutability via transferability of tolerances
Regularity and transitivity of local-automorphism semigroups of locally finite forests
Regularity in p-algebras and p-semilattices
Regularity of algebras with applications to congruence class geometry