Semimodules and semirings admitting a maximal factorization

Abstract

The notion of a maximal factorization of a K-semimodule M is introduced, and several necessary and sufficient conditions for M admitting a maximal factorization are given. By using such conditions, the characterizations of the semirings that admit a maximal factorization of finite dimension are obtained. Also, some special cases are considered.

Keywords:

• maximal factorization
• least right M-divisor
• cyclic θ-direct decomposition
• min-direct union of maximal intervals
• F-cancellative semimodule
• greatest left K-divisor
• gcld condition

2000 AMS Subject Classifications :

• 08A70
• 16Y60

Acknowledgements

The author acknowledges the suggestions and corrections of the referees and the editors which resulted in improvements of this paper. Partially supported by grants of Natural Scientific Foundation of Hunan (No. 06JJ2025), Scientific Foundation of Education Department of Hunan (No. 05A014) and 973 Project of China (No. 2003CB317001).