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Research Article | Open Access

An introduction to the theory of OBCI-algebras

Eunsuk Yang1, Eun Hwan Roh2, Young Bae Jun3( )
Department of Philosophy, Jeonbuk National University, Jeonju 54896, Korea
Department of Mathematics Education, Chinju National University of Education, Jinju 52673, Korea
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
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Abstract

The purpose of this paper was to introduce the concept of "OBCI-algebras" as a partially ordered generalization of BCI-algebras. The notion of OBCI-algebras was introduced, and related properties were investigated. The notions of OBCI-subalgebras and (closed) OBCI-filters of OBCI-algebras were defined and the relationship between the OBCI-subalgebras and OBCI-filters was discussed. In addition, the direct product OBCI-algebra was discussed, and the OBCI-filter related to it was also addressed.

Keywords

OBCI-algebrasubalgebraOBCI-subalgebrafilter(closed) OBCI-filter
CLC number: 03B05, 03G25, 06F35

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AIMS Mathematics
Volume 9 Issue 12,
December 2024
Pages 36336-36350
DOI: 10.3934/math.20241723

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Cite this article:
Yang E, Roh EH, Jun YB. An introduction to the theory of OBCI-algebras. AIMS Mathematics, 2024, 9(12): 36336-36350. https://doi.org/10.3934/math.20241723

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Received: 12 August 2024
Revised: 21 November 2024
Accepted: 18 December 2024
Published: 15 December 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)