Permutability, Distributivity of Equivalence Relations and Direct Products
Polynomials in idempotent commutative groupoids [Book]
Poproduct of Lattices and Sorkin's Theorem
Preservation Theorems for Limits of Structures and Global Sections of Sheaves of Structures.
Produit symétrisé
Propriétés catégorielles dans la théorie des algèbres universelles
Propriétés de permanence et existence de réalisations minimales pour les algèbres multisortes
Remarks on C-independence in Cartesian products of abstract algebras
Remarks on -independence of Stone algebras
Remarks on tolerance algebras
Représentations matricielles des séries d'arbre reconnaissables
Retracts and Q-independence
A non-empty set X of a carrier A of an algebra A is called Q-independent if the equality of two term functions f and g of the algebra A on any finite system of elements a₁,a₂,...,aₙ of X implies f(p(a₁),p(a₂),...,p(aₙ)) = g(p(a₁),p(a₂),...,p(aₙ)) for any mapping p ∈ Q. An algebra B is a retract of A if B is the image of a retraction (i.e. of an idempotent endomorphism of B). We investigate Q-independent subsets of algebras which have a retraction in their set of term functions.
Sets with two associative operations
In this paper we consider duplexes, which are sets with two associative binary operations. Dimonoids in the sense of Loday are examples of duplexes. The set of all permutations carries a structure of a duplex. Our main result asserts that it is a free duplex with an explicitly described set of generators. The proof uses a construction of the free duplex with one generator by planary trees.
Sheaf Spaces and Sheaves of Universal Algebras.
Some algebraic properties of weakly compact and compact cardinals
Some old and new problems in the independence theory
Structure of free algebras
Subdirectly irreducible groupoids in some varieties
Subdirectly irreducible non-idempotent left symmetric left distributive groupoids
We study groupoids satisfying the identities x·xy = y and x·yz = xy·xz. Particularly, we focus our attention at subdirectlyirreducible ones, find a description and charecterize small ones.
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