On Exact Sequence of Semimodules over Semirings. (30th July 2013)

• Record Type: Journal Article
• Authors: Chaudhari, Jayprakash Ninu; Bonde, Dipak Ravindra
• Other Names: Koshlukov P. Academic Editor.; Li H. Academic Editor.
• Is Part Of: ISRN algebra. Volume 2013(2013)
• Publication Date: 2013-07-30
• Subjects: Algebra -- Periodicals; Algebra; Periodicals; Electronic journals; 512
• DOI: 10.1155/2013/156485
• Languages: English
• ISSNs: 2090-6285

Abstract

Abstract : We introduce the notion of exact sequence of semimodules over semirings using maximal homomorphisms and generalize some results of module theory to semimodules over semirings. Indeed, we prove, "If 0 → L → f M → g N → 0 is a split exact sequence of R -semimodules and maximal R -semimodule homomorphisms with K e r ( g ) is a strong subsemimodule of M, then M ≅ L ⊕ N ". Also, some results of commutative diagram of R -semimodules and maximal R -homomorphisms having exact rows are obtained.