On the Core of Second Smarandache Bol Loops

Let (G, ·) be a loop. A loop (GH, ·) is called a special loop of (G, ·) if the pair (H, ·) is an arbitrary a non-empty subloop of (G, ·). In general, (GH, ·) is called second Smarandache Bol loop (S2ndBL) if it obey the identity (xs · z)s = x(sz · s) for all s ∈ H and x,z ∈ G. This paper presents so...

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Bibliographic Details
Published in:International journal of mathematical combinatorics 2023-06, Vol.2, p.18-30
Main Authors: Osoba, B, Oyebo, Y T
Format: Article
Language:English
Subjects:
Algebra
Number theory
Online Access:Get full text
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Summary:Let (G, ·) be a loop. A loop (GH, ·) is called a special loop of (G, ·) if the pair (H, ·) is an arbitrary a non-empty subloop of (G, ·). In general, (GH, ·) is called second Smarandache Bol loop (S2ndBL) if it obey the identity (xs · z)s = x(sz · s) for all s ∈ H and x,z ∈ G. This paper presents some algebraic characterizations of the core of a second Smarandache Bol loop (S2ndBL). Some results in this paper extend or generalize the results of the classical studies of the core of a Bol loop. The conditions for the core of S2ndBL to be left symmetric, left(right) idempotents, left self-distributive, and flexible was shown. A necessary and sufficient condition for a core of (S2ndBL) to be right(left) alternative property was revealed. The characterization of S-isotopic and S-isomorphic invariance was also presented in this paper.
ISSN:1937-1055
1937-1047