-quasigroups isotopic to Moufang loops
Faithful homogeneous spaces over commutative groups and TST-spaces.
A set Q is a faithful homogeneous space over a commutative group iff there is a family S of mappings such that (Q,S) is a TST-space.
Feebly canonical and 1-hypergroups
Finite AG-groupoid with left identity and left zero.
Finite monogenic distributive systems
Finite simple zeropotent paramedial groupoids
The study of paramedial groupoids (with emphasis on the structure of simple paramedial groupoids) was initiated in [1] and continued in [2], [3] and [5]. The aim of the present paper is to give a full description of finite simple zeropotent paramedial groupoids (i.e., of finite simple paramedial groupoids of type (II)—see [2]). A reader is referred to [1], [2], [3] and [7] for notation and various prerequisites.
Fortified Join hypergroups
Foundations of the Theory of Groupoids and Groups [Book]
F-quasigroups and generalized modules
In Kepka T., Kinyon M.K., Phillips J.D., The structure of F-quasigroups, J. Algebra 317 (2007), 435–461, we showed that every F-quasigroup is linear over a special kind of Moufang loop called an NK-loop. Here we extend this relationship by showing an equivalence between the class of (pointed) F-quasigroups and the class corresponding to a certain notion of generalized module (with noncommutative, nonassociative addition) for an associative ring.
F-quasigroups isotopic to groups
In Kepka T., Kinyon M.K., Phillips J.D., The structure of F-quasigroups, math.GR/0510298, we showed that every loop isotopic to an F-quasigroup is a Moufang loop. Here we characterize, via two simple identities, the class of F-quasigroups which are isotopic to groups. We call these quasigroups FG-quasigroups. We show that FG-quasigroups are linear over groups. We then use this fact to describe their structure. This gives us, for instance, a complete description of the simple FG-quasigroups. Finally,...
Free commutative idempotent abelian groupoids and quasigroups
Free entropic groupoids
Free groupoids with axioms of the form and/or .
Free groupoids with . II.
Free Objects in Primitive Varieties of N-groupoids
Free products of n-groups
Frobenius n-group algebras
Frobenius algebras play an important role in the representation theory of finite groups. In the present work, we investigate the (quasi) Frobenius property of n-group algebras. Using the (quasi-) Frobenius property of ring, we can obtain some information about constructions of module category over this ring ([2], p. 66-67).
Fully fuzzy prime semigroups.
Functional equations of generalized associativity, bisymmetry, transitivity and distributivity.
Functional equations on Sturm-Liouville hypergroups.