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<p>In this paper, we introduce inverse commutative residuated lattices and study some special ones, namely, totally ordered inverse commutative residuated lattices. After obtaining some properties of such inverse commutative residuated lattices, we establish a structure theorem for totally ordered inverse commutative residuated lattices. As an application, we make use of the structure theorem to prove that the variety generated by all totally ordered inverse commutative residuated lattices is arithmetical, congruence extensible and <i>e</i>-regular.</p>

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Totally ordered inverse commutative residuated lattices

  • 期刊论文

  • 发表日期：

    2026年3月6日

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  • Wei Chen,
  • Shangyang Wu

摘要

In this paper, we introduce inverse commutative residuated lattices and study some special ones, namely, totally ordered inverse commutative residuated lattices. After obtaining some properties of such inverse commutative residuated lattices, we establish a structure theorem for totally ordered inverse commutative residuated lattices. As an application, we make use of the structure theorem to prove that the variety generated by all totally ordered inverse commutative residuated lattices is arithmetical, congruence extensible and e-regular.