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