Partitions in ternars
Permutable groupoids
Pinned-flags of some operations on fuzzy subgroups.
Plenary stable quasigroups
Some results are obtained for quasigroups in which the operation of iterated squaring always leads to stability irrespective of the initial element.
Pointwise and global sums and negatives of binary relations.
Pointwise and global sums and negatives of translation relations.
Polyabelian loops and Boolean completeness
We consider the question of which loops are capable of expressing arbitrary Boolean functions through expressions of constants and variables. We call this property Boolean completeness. It is a generalization of functional completeness, and is intimately connected to the computational complexity of various questions about expressions, circuits, and equations defined over the loop. We say that a loop is polyabelian if it is an iterated affine quasidirect product of Abelian groups; polyabelianness...
Polygroupes et Certaines de leurs Proprietes
Polynomial functions over finite monoids.
Poset valued varieties.
Possible orders of nonassociative Moufang loops
The paper surveys the known results concerning the question: “For what values of does there exist a nonassociative Moufang loop of order ?” Proofs of the newest results for odd, and a complete resolution of the case even are also presented.
Powers and alternative laws
A groupoid is alternative if it satisfies the alternative laws and . These laws induce four partial maps on
Powers of elements in Jordan loops
A Jordan loop is a commutative loop satisfying the Jordan identity . We establish several identities involving powers in Jordan loops and show that there is no nonassociative Jordan loop of order .
Presolid varieties of n-semigroups
he class of all M-solid varieties of a given type t forms a complete sublattice of the lattice ℒ(τ) of all varieties of algebrasof type t. This gives a tool for a better description of the lattice ℒ(τ) by characterization of complete sublattices. In particular, this was done for varieties of semigroups by L. Polák ([10]) as well as by Denecke and Koppitz ([4], [5]). Denecke and Hounnon characterized M-solid varieties of semirings ([3]) and M-solid varieties of groups were characterized by Koppitz...
Products of all elements in a loop and a framework for non-associative analogues of the Hall-Paige conjecture.
Products of partially ordered quasigroups
We describe necessary and sufficient conditions for a direct product and a lexicographic product of partially ordered quasigroups to be a positive quasigroup. Analogous questions for Riesz quasigroups are studied.
Projection representable relations on Menger -semigroups
Abstract characterizations of relations of nonempty intersection, inclusion end equality of domains for partial -place functions are presented. Representations of Menger -semigroups by partial -place functions closed with respect to these relations are investigated.
Pseudoautomorphisms of Bruck loops and their generalizations
We show that in a weak commutative inverse property loop, such as a Bruck loop, if is a right [left] pseudoautomorphism with companion , then [] must lie in the left nucleus. In particular, for any such loop with trivial left nucleus, every right pseudoautomorphism is an automorphism and if the squaring map is a permutation, then every left pseudoautomorphism is an automorphism as well. We also show that every pseudoautomorphism of a commutative inverse property loop is an automorphism, generalizing...
Pseudo-complemented distributive groupoids
Quadratic Level Quasigroup Equations With Four Variables II: the Lattice of Varieties