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<p>In 2023, Radfar and Rezaei (J Algebr Hyperstructures Log Algebr 4(2):167–187, 2023) introduced the concept of <i>left distributive pseudo-BI algebras</i> as a non-commutative generalization of BI algebras. In this paper, we investigate the interplay between <i>filters</i> and <i>left congruences</i> in these algebras. Specifically, we prove that every filter <i>F</i> in a left distributive pseudo-BI algebra <i>A</i> induces a left congruence on <i>A</i>, and conversely, every left congruence on <i>A</i> corresponds to a unique filter. These results establish a one-to-one correspondence between the algebraic and order-theoretic structures of pseudo-BI algebras. We provide supporting examples and discuss their implications for applications in non-classical logics and related algebraic systems.</p>

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Filters and left congruences in pseudo-BI algebras

  • 期刊论文

  • 发表日期：

    2025年12月11日

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  • Akbar Rezaei,
  • Daniel A. Romano

摘要

In 2023, Radfar and Rezaei (J Algebr Hyperstructures Log Algebr 4(2):167–187, 2023) introduced the concept of left distributive pseudo-BI algebras as a non-commutative generalization of BI algebras. In this paper, we investigate the interplay between filters and left congruences in these algebras. Specifically, we prove that every filter F in a left distributive pseudo-BI algebra A induces a left congruence on A, and conversely, every left congruence on A corresponds to a unique filter. These results establish a one-to-one correspondence between the algebraic and order-theoretic structures of pseudo-BI algebras. We provide supporting examples and discuss their implications for applications in non-classical logics and related algebraic systems.