Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
On pseudoisomorphy and distributivity of quasigroups
Authors: Fedir M. Sokhatsky
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Abstract
A repeated bijection in an isotopism of quasigroups is called a \emph{companion} of the third component. The last is called a \emph{pseudoisomorphism} with the companion. Isotopy coincides with pseudoisomorphy\footnote{isotopy, pseudoisomorphy, isomorphy denote relation among groupoids and isotopism, psuedoisomorphism, isomorphism are the corresponding sequence of bijections}\; in the class of inverse property loops and with isomorphy in the class of commutative inverse property loops. This result is a generalization of the corresponding theorem for commutative Moufang loops. A notion of middle distributivity is introduced: a quasigroup is \emph{middle distributive} if all its middle translations are automorphisms. In every quasigroup two identities of distributivity (left, right and middle) imply the third. This fact and some others help us to find a short proof of a theorem which gives necessary and sufficient conditions for a quasigroup to be distributive. There is but a slight difference between this theorem and the well-known Belousov's theorem.Vasyl Poryk, 5, ap.37, Vinnytsia, 21021
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Fulltext
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Contents
- Lacunary Ideal Convergence in Probabilistic Normed Space
- The multiplicative Zagreb co-indices on two graph operators
- On Lagrange algorithm for reduced algebraic irrationalities
- Asymmetric ID-Based Encryption System, Using an Explicit Pairing Function of the Reciprocity Law
- Almost periodicity of functions on universal algebras
- Lattice of all topologies of countable module over countable rings
- Stationary Nash Equilibria for Average Stochastic Games with Finite State and Action Spaces
- General form transversals in groups
- Operations on level graphs of bipolar fuzzy graphs
- On pseudoisomorphy and distributivity of quasigroups
- On spectrum of medial T2-quasigroups
