Bulletin of the
Korean Mathematical Society BKMS

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 $A=[a_{i,j}]$ is idempotent if and only if all $a_{i,j}$-patterns of $A$ are idempotent matrices over the binary Boolean algebra $\b_1=\{0,1\}$. 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.

Keywords: semiring, idempotent, frame, rectangle part, line part

MSC numbers: 15A21, 15A33