Free objects in triangular matrix varieties and quiver algebras over semirings

نویسندگان

چکیده

We study the free objects in variety of semigroups and monoids generated by monoid all n×n upper triangular matrices over a commutative semiring. obtain explicit representations these, as multiplicative subsemigroups quiver algebras polynomial semirings. A case particular interest is where n=2 semiring tropical semifield, coincides with that bicyclic (or equivalently, monogenic inverse monoid); here we are faithful this inside semidirect product acting on semilattice. apply these to answer several questions, including when given varieties locally finite.

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ژورنال

عنوان ژورنال: Journal of Algebra

سال: 2022

ISSN: ['1090-266X', '0021-8693']

DOI: https://doi.org/10.1016/j.jalgebra.2021.08.030