Results 1 to 10 of about 48 (22)
Embedding Alexander quandles into groups [PDF]
Journal of knot theory and its ramifications, 2022 For any twisted conjugate quandle Q, and in particular any Alexander quandle, there exists a group G such that Q is embedded into the conjugation quandle of G. 1. EMBEDDABLE QUANDLES A non-empty set Q equipped with a binary operation Q×Q → Q, (x,y) 7→ x∗
Toshiyuki Akita
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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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Fibonacci sequences in groupoids
Advances in Differential Equations, 2012 In this article, we consider several properties of Fibonacci sequences in arbitrary groupoids (i.e., binary systems). Such sequences can be defined in a left-hand way and a right-hand way.
Jeong Soon Han, H. Kim, J. Neggers
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Generalized Fibonacci sequences in groupoids
Advances in Differential Equations, 2013 In this paper, we introduce the notion of generalized Fibonacci sequences over a groupoid and discuss it in particular for the case where the groupoid contains idempotents and pre-idempotents.
H. Kim, J. Neggers, K. So
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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 the work of F. W. 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 ...
F. Guzmán
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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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Congruences and decompositions of AG$^{**}$-groupoids
, 2018 We introduce the concept of completely left inverse AG -groupoids and study some basic congruences and a congruence pair by means of the kernel and trace approach of completely left inverse AG -groupoids.
W. Khan, Faisal Yousafzai, K. Hila
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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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