Algebraic structure of square matrices over residuated lattices

Year 2019, Volume: 68 Issue: 2, 2216 - 2237, 01.08.2019

Arsham Borumand Saeid E Eslami S Balaei

https://doi.org/10.31801/cfsuasmas.423277

Abstract

In this paper, we introduce the algebra Mnn(L) of square matrices over residuated lattice L. The operations are induced by the corresponding operations of L. It is shown that the defined algebra behaves like a residuated lattice, but there are some slight differences. The properties of this algebra with respect to special residuated lattices are
investigated. The notions of filter and ideal together with their roles are specified.

Keywords

Residuated lattices, matrices over residuated lattices, operations on matrices, filter, ideal

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