Certain numerical results in non‑ associative structures

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Azizi Behnam; DOOSTIE HOSSEIN

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Journal: MATHEMATICAL SCIENCES Year:2019 | Volume:13 | Issue:1 Page(s): 27-32

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Title

Certain numerical results in non‑ associative structures

Author(s)

Azizi Behnam | DOOSTIE HOSSEIN | Issue Writer Certificate

Keywords

Loop

Moufang loop

nth-commutativity degree

Abstract

The finite non-commutative and non-associative algebraic structures are indeed one of the special structures for their probabilistic results in some branches of mathematics. For a given integer n ≥ 2, the nth-commutativity degree of a finite algebraic structure S, denoted by Pn(S), is the probability that for chosen randomly two elements x and y of S, the relator xny = yxn holds. This degree is specially a recognition tool in identifying such structures and studied for associative algebraic structures during the years. In this paper, we study the nth-commutativity degree of two infinite classes of finite Loops, which are non-commutative and non-associative. Also by deriving explicit expressions for nth-commutativity degree of these Loops, we will obtain best upper bounds for this probability.

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APA: Copy

Azizi, Behnam, & DOOSTIE, HOSSEIN. (2019). Certain numerical results in non‑ associative structures. MATHEMATICAL SCIENCES, 13(1), 27-32. SID. https://sid.ir/paper/322731/en

Vancouver: Copy

Azizi Behnam, DOOSTIE HOSSEIN. Certain numerical results in non‑ associative structures. MATHEMATICAL SCIENCES[Internet]. 2019;13(1):27-32. Available from: https://sid.ir/paper/322731/en

IEEE: Copy

Behnam Azizi, and HOSSEIN DOOSTIE, “Certain numerical results in non‑ associative structures,” MATHEMATICAL SCIENCES, vol. 13, no. 1, pp. 27–32, 2019, [Online]. Available: https://sid.ir/paper/322731/en

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