Identities and deleting maps on quasigroups
Identities and the group of isostrophisms
In this paper we reexamine the concept of isostrophy. We connect it to the notion of term equivalence, and describe the action of dihedral groups that are associated with loops by means of isostrophy. We also use it to prove and present in a new way some well known facts on -inverse loops and middle Bol loops.
Incomplete idempotent Schröder quasigroups and related packing designs.
Infinite independent systems of identities of alternative commutative algebra over a field of characteristic three
Let 𝔄₃ denote the variety of alternative commutative (Jordan) algebras defined by the identity x³ = 0, and let 𝔖₂ be the subvariety of the variety 𝔄₃ of solvable algebras of solviability index 2. We present an infinite independent system of identities in the variety 𝔄₃ ∩ 𝔖₂𝔖₂. Therefore we infer that 𝔄₃ ∩ 𝔖₂𝔖₂ contains a continuum of infinite based subvarieties and that there exist algebras with an unsolvable words problem in 𝔄₃ ∩ 𝔖₂𝔖₂. It is worth mentioning that these results were...
Infinite simple Bol loops
If the left multiplication group of a loop is simple, then the loop is simple. We use this observation to give examples of infinite simple Bol loops.
Intersection preserving finite embedding theorems fo partial quasigroups.
Inverse property, flexible loops
Uno dei metodi migliori per scoprire le proprietà di un cappio chiuso è studiarne il gruppo di moltiplicazione [3], [4]. In questo breve saggio descriviamo i gruppi di moltiplicazione di una classe importante di cappi, e cioè di quella dei cappi flessibili che posseggono la proprietà inversa.
Inverse property of nonassociative abelian extensions
Our paper deals with the investigation of extensions of commutative groups by loops so that the quasigroups that result in the multiplication between cosets of the kernel subgroup are T-quasigroups. We limit our study to extensions in which the quasigroups determining the multiplication are linear functions without constant term, called linear abelian extensions. We characterize constructively such extensions with left-, right-, or inverse properties using a general construction according to an...
Invertibility criterion of composition of two multiary quasigroups
We study invertibility of operations that are composition of two operations of arbitrary arities. We find the criterion for quasigroups and specifications for -quasigroups. For this purpose we introduce notions of perpendicularity of operations and hypercubes. They differ from the previously introduced notions of orthogonality of operations and hypercubes [Belyavskaya G., Mullen G.L.: Orthogonal hypercubes and -ary operations, Quasigroups Related Systems 13 (2005), no. 1, 73–86]. We establish...
Irreducible Belousov equations on quasigroups