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<p>This paper deals with analogues of two famous theorems of Birkhoff, the subdirect representation and varieties theorems of algebras, in the context of reduced tonoid matrices. More precisely, we first introduce tonoid matrices and isotonic ordered matrices. We next provide subdirect product representations for reduced tonoid and isotonic ordered matrices. We then introduce analogues of the varieties theorems for algebras in the context of reduced tonoid and isotonic ordered matrices. Finally, we extend them to their corresponding quasi-varieties theorems.</p>

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Some Theorems of Birkhoff in Tonoid Matrices

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Eunsuk Yang

摘要

This paper deals with analogues of two famous theorems of Birkhoff, the subdirect representation and varieties theorems of algebras, in the context of reduced tonoid matrices. More precisely, we first introduce tonoid matrices and isotonic ordered matrices. We next provide subdirect product representations for reduced tonoid and isotonic ordered matrices. We then introduce analogues of the varieties theorems for algebras in the context of reduced tonoid and isotonic ordered matrices. Finally, we extend them to their corresponding quasi-varieties theorems.