Volume 10, Issue 3 (11-2024)
mmr 2024, 10(3): 52-71 |
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Radfar A. Classification BI-algebras of order less than 5 with their ideals. mmr 2024; 10 (3) :52-71
URL: http://mmr.khu.ac.ir/article-1-3326-en.html
URL: http://mmr.khu.ac.ir/article-1-3326-en.html
, ateferadfar@yahoo.com
Abstract: (131 Views)
In this paper, BI-algebras of order 2, 3, and 4 are characterized, and the Cayley tables are presented up to isomorphism. It is shown that there is one BI-algebra of order 2, two BI-algebras of order 3, and eight BI-algebras of order 4 up to isomorphism. Moreover, it is proved that every commutative and right-distributive BI-algebra is a BCK-algebra. In addition, we show which ones are commutative, transitive, and distributive. All ideals of every BI-algebra in this paper are presented.
Keywords: BI-algbera, distributive, commutative, BCK-algebra, Hilbert algebra, Dual Hilbert algebra
Type of Study: S |
Subject:
alg
Received: 2023/04/12 | Revised: 2024/11/11 | Accepted: 2024/08/26 | Published: 2024/11/6 | ePublished: 2024/11/6
Received: 2023/04/12 | Revised: 2024/11/11 | Accepted: 2024/08/26 | Published: 2024/11/6 | ePublished: 2024/11/6
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