STRUCTURES OF IDEMPOTENT MATRICES OVER CHAIN SEMIRINGS

Title & Authors
STRUCTURES OF IDEMPOTENT MATRICES OVER CHAIN SEMIRINGS
Kang, Kyung-Tae; Song, Seok-Zun; Yang, Young-Oh;

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 $\small{A=[a_{i,j}]}$ is idempotent if and only if all $\small{a_{i,j}}$-patterns of A are idempotent matrices over the binary Boolean algebra $\small{\mathbb{B}_1={0,1}}$. 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;
Language
English
Cited by
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2.
On Decompositions of Matrices over Distributive Lattices, Journal of Applied Mathematics, 2014, 2014, 1
3.
Idempotent matrices over antirings, Linear Algebra and its Applications, 2009, 431, 5-7, 823
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