IJPAM: Volume 75, No. 2 (2012)
Department of Mathematics
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 .
Received: June 14, 2011
AMS Subject Classification: 20M10, 15A09, 16Y60
Key Words and Phrases: decomposition, matrix, finite chain, subdirect product, semigroup, semiring
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395