On permanents of matrices over a commutative additively idempotent semiring

TL;DR

This paper explores properties, inequalities, and adjoint matrices of permanents over matrices in a commutative additively idempotent semiring, generalizing results from fuzzy, lattice, and incline matrices.

Contribution

It introduces new properties and inequalities for permanents over such semirings, extending existing theories to a broader algebraic context.

Findings

Established properties and characterizations of permanents over R

Derived several inequalities for permanents

Analyzed adjoint matrices over R

Abstract

Let $R$ be a commutative additively idempotent semiring. In this paper, some properties and characterizations for permanents of matrices over $R$ are established, and several inequalities for permanents are given. Also, the adjiont matrices of matriecs over $R$ are considered. Partial results obtained in this paper generalize the corresponding ones on fuzzy matrices, on lattice matrices and on incline matrices.