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Quantum quasigroups and quantum loops are self-dual objects providing a general framework for the nonassociative extension of quantum group techniques. This paper examines their one-sided analogues, which are not self-dual. Just as quantum quasigroups are the “quantum” version of quasigroups, so one-sided quantum quasigroups are the “quantum” version of left or right quasigroups.

Quantum quasigroups and quantum loops are self-dual objects providing a general framework for the nonassociative extension of quantum group techniques. This paper examines their one-sided analogues, which are not self-dual. Just as quantum quasigroups are the "quantum" version of quasigroups, so one-sided quantum quasigroups are the "quantum" version of left or right quasigroups. [ABSTRACT FROM AUTHOR]

In this article, we associate new invariants called pseudohomology and pseudo-cohomology groups to right quasigroups and in turn to geometric spaces with natural quasigroup structures and to general extensions. It initiates a program to differentiate different types of general extensions. [ABSTRACT FROM AUTHOR]

Abstract: Connections of some groupoid identities with the quasigroup and Latin square properties are investigated using combinatorial methods. [Copyright &y& Elsevier]

In this article we prove that there does not exist a subgroup H of a finite group G such that the number of isomorphism classes of right transversals of H in G is two. [ABSTRACT FROM AUTHOR]