# IJPAM: Volume 75, No. 2 (2012)

DECOMPOSITIONS OF MATRICES OVER A FINITE CHAIN

Yizhi Chen, Haiqing Wang, Hui Luo
Department of Mathematics
Huizhou University
Huizhou, Guangdong, 516007, P.R. CHINA

Abstract. Let denote a finite chain, be the additive semigroup of all the matrices over . In this paper, we firstly give some subdirect decompositions of a finite chain , and then show that if there is a subdirect embedding from to the direct product of subchains , then there will be a corresponding subdirect embedding from the semigroup to semigroup . Based on the above results, it is also proved that a matrix can be decomposed into the sum of matrices over some special subchains of which generalizes and extends the corresponding results obtained by [1].

AMS Subject Classification: 20M10, 15A09, 16Y60

Key Words and Phrases: decomposition, matrix, finite chain, subdirect product, semigroup, semiring