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<p>In this paper we describe the implicative subreducts of RWH-algebras, which will be called IRWH-algebras, by using some techniques considered to the study of the implicative-infimum subreducts of weak Heyting algebras. More precisely, we present a quasi-equational base for the quasivariety of IRWH-algebras. We also introduce open implicative filters in order to study the lattice of relative congruences of IRWH-algebras. Moreover, we introduce and study irreducible open implicative filters with the aim to study the quasivariety generated by the class of the totally ordered IRWH-algebras.</p>

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On the Implicative Subreducts of RWH-Algebras

  • 期刊论文

  • 发表日期：

    2025年11月24日

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  • Jose L. Castiglioni,
  • Hernan J. San Martín

摘要

In this paper we describe the implicative subreducts of RWH-algebras, which will be called IRWH-algebras, by using some techniques considered to the study of the implicative-infimum subreducts of weak Heyting algebras. More precisely, we present a quasi-equational base for the quasivariety of IRWH-algebras. We also introduce open implicative filters in order to study the lattice of relative congruences of IRWH-algebras. Moreover, we introduce and study irreducible open implicative filters with the aim to study the quasivariety generated by the class of the totally ordered IRWH-algebras.