Results 1 to 10 of about 188 (47)
Pentagonal quasigroups, their translatability and parastrophes
Open Mathematics, 2021 Any pentagonal quasigroup QQ is proved to have the product xy=φ(x)+y−φ(y)xy=\varphi \left(x)+y-\varphi (y), where (Q,+)\left(Q,+) is an Abelian group, φ\varphi is its regular automorphism satisfying φ4−φ3+φ2−φ+ε=0{\varphi }^{4}-{\varphi }^{3}+{\varphi }^
Dudek Wieslaw A., Monzo Robert A. R.
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Associativity of the Commutator Operation in Groups [PDF]
, 2008 The study of associativity of the commutator operation in groups goes back to some work of Levi in 1942. In the 1960's Richard J. Thompson created a group F whose elements are representatives of the generalized associative law for an arbitrary binary ...
Guzman, Fernando
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Cohomology and extensions of braces [PDF]
, 2016 Braces and linear cycle sets are algebraic structures playing a major role in the classification of involutive set-theoretic solutions to the Yang-Baxter equation. This paper introduces two versions of their (co)homology theories.
Lebed, V., Vendramin, L.
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Discussiones Mathematicae - General Algebra and Applications, 2017 In this paper, the notion of a QI-algebra is introduced which is a generalization of a BI-algebra and there are studied its properties. We considered ideals, congruence kernels in a QI-algebra and characterized congruence kernels whenever a QI-algebra is
Bandaru Ravi Kumar
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Translatability and translatable semigroups
Open Mathematics, 2018 The concept of a k-translatable groupoid is explored in depth. Some properties of idempotent k-translatable groupoids, left cancellative k-translatable groupoids and left unitary k-translatablegroupoids are proved. Necessary and sufficient conditions are
Dudek Wieslaw A., Monzo Robert A. R.
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 In this paper, we introduce a new algebra, called a BI-algebra, which is a generalization of a (dual) implication algebra and we discuss the basic properties of BI-algebras, and investigate ideals and congruence relations.
Saeid Arsham Borumand +2 more
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Fuzzy soft set approach to ideal theory of regular AG-groupoids
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 This paper aims to apply fuzzy sets and soft sets in combination to investigate algebraic properties of regular AG-groupoids. We initiate (∈γ; ∈γ qδ)-fuzzy soft left ideals (right ideals, bi-ideals and quasi-ideals) over AG-groupoids and explore some ...
Feng Feng +4 more
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Holomorph of generalized Bol loops II
, 2015 The notion of the holomorph of a generalized Bol loop (GBL) is characterized afresh. The holomorph of a right inverse property loop (RIPL) is shown to be a GBL if and only if the loop is a GBL and some bijections of the loop are right (middle) regular ...
Jaíyéolá, Tèmít\dóp\dé Gbóláhàn +1 more
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, 2016 In a paper published in 2012, the second author extended the well-known fact that Boolean algebras can be defined using only implication and a constant, to De Morgan algebras-this result led him to introduce, and investigate (in the same paper), the ...
Cornejo, Juan M. +1 more
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Two- and three-cocycles for Laver tables [PDF]
, 2014 We determine all 2- and 3-cocycles for Laver tables, an infinite sequence of finite structures obeying the left-selfdistributivity law; in particular, we describe simple explicit bases.
Dehornoy, Patrick, Lebed, Victoria
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