Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
On Latin squares of polynomially complete quasigroups and quasigroups generated by shifts
Authors: V. A. Artamonov, S. Chakrabarti, S. Gangopadhyay and S. K. Pal
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Abstract
We develop some methods and algorithms for checking the polynomial completeness property of some finite quasigroups by considering their corresponding Latin square representations. It is shown that polynomially complete quasigroups are simple and non-T-quasigroups. We study cyclic decompositions of permutations related to rows and columns of Latin squares of non-simple quasigroups and of T-quasigroups. Here we develop the criteria for the polynomial completeness of finite quasigroups based on this study.Fulltext
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Contents
- On Latin squares of polynomially complete quasigroups and quasigroups generated by shifts
- Hom-Bol algebras
- Ascending chain conditions on principal left and right ideals for semidirect products of ordered semigroups
- On regular medial division algebras
- Contractions of quasigroups and Latin squares
- On 2-absorbing semimodules
- Strong forms of orthogonality for sets of frequency hypercubes
- A still shorter axiom for trimedial quasigroups
- Clifford congruences on perfect semigroups
- E-disjunctive semigroups and idempotent pure congruences
- Groups with the same orders and large character degrees as PGL(2,9)
- Coset diagrams of the action of a certain Bianchi group on PL(Fp)
- Automorphisms of abelian n-ary groups
- Free products of dimonoids
