On free commutative groupoids.
On full partial quasigroups of finite order and local cardinal maximum codes.
On fuzzy points in semigroups.
On GD-groupoids with application to n-ary quasigroups.
On Generalized (i, j)-Modular Quasigroups
On generalized (i,,j)-modular quasigroups.
On Hall planar ternary rings with ordered carrier sets
On homomorphisms of fuzzy groups.
On ideals in regular ternary semigroups
In this paper we study some interesting properties of regular ternary semigroups, completely regular ternary semigroups, intra-regular ternary semigroups and characterize them by using various ideals of ternary semigroups.
On infinitary quasigroups.
On left distributive left idempotent groupoids
We study the groupoids satisfying both the left distributivity and the left idempotency laws. We show that they possess a canonical congruence admitting an idempotent groupoid as factor. This congruence gives a construction of left idempotent left distributive groupoids from left distributive idempotent groupoids and right constant groupoids.
On Lie semiheaps and ternary principal bundles
We introduce the notion of a Lie semiheap as a smooth manifold equipped with a para-associative ternary product. For a particular class of Lie semiheaps we establish the existence of left-invariant vector fields. Furthermore, we show how such manifolds are related to Lie groups and establish the analogue of principal bundles in this ternary setting. In particular, we generalise the well-known ‘heapification’ functor to the ambience of Lie groups and principal bundles.
On loops that are abelian groups over the nucleus and Buchsteiner loops
We give sufficient and in some cases necessary conditions for the conjugacy closedness of provided the commutativity of . We show that if for some loop , and are abelian groups, then is a CC loop, consequently has nilpotency class at most three. We give additionally some reasonable conditions which imply the nilpotency of the multiplication group of class at most three. We describe the structure of Buchsteiner loops with abelian inner mapping groups.
On loops whose inner permutations commute
Multiplication groups of (finite) loops with commuting inner permutations are investigated. Special attention is paid to the normal closure of the abelian permutation group.
On Maps x ... xn and the Isotopy-Isomorphy Property of Moufang Loops (Short Communication)
On Maps x-xn and the Isotopy-Isomorphy Property of Moufang Loops
On median point of the system of elements of -structure
On middle universal weak and cross inverse property loops with equal length of inverse cycles.
On Mikheev's construction of enveloping groups
Mikheev, starting from a Moufang loop, constructed a groupoid and reported that this groupoid is in fact a group which, in an appropriate sense, is universal with respect to enveloping the Moufang loop. Later Grishkov and Zavarnitsine gave a complete proof of Mikheev's results. Here we give a direct and self-contained proof that Mikheev's groupoid is a group, in the process extending the result from Moufang loops to Bol loops.
On minimization theorems for polyadic groups H-derived from groups