Structures of idempotent matrices over chain semirings
Bull. Korean Math. Soc. 2007 Vol. 44, No. 4, 721-729
Published online December 1, 2007
Kyung-Tae Kang, Seok-Zun Song, and Young-Oh Yang
Cheju National University, Cheju National University, Cheju National University
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 $A=[a_{i,j}]$ 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
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