STRUCTURES OF IDEMPOTENT MATRICES OVER CHAIN SEMIRINGS

Abstract

In this paper, we have characterizations of idempotent matrices over general Boolean algebras and chain semirings. As a consequence, we obtain that a fuzzy matrix <TEX>$A=[a_{i,j}]$</TEX> is idempotent if and only if all <TEX>$a_{i,j}$</TEX>-patterns of A are idempotent matrices over the binary Boolean algebra <TEX>$\mathbb{B}_1={0,1}$</TEX>. Furthermore, it turns out that a binary Boolean matrix is idempotent if and only if it can be represented as a sum of line parts and rectangle parts of the matrix.