Table of Contents
ISRN Algebra
Volume 2013 (2013), Article ID 156485, 5 pages
http://dx.doi.org/10.1155/2013/156485
Research Article

On Exact Sequence of Semimodules over Semirings

1Department of Mathematics, M. J. College, Jalgaon 425002, India
2Department of Mathematics, ACS College, Dharangaon 425105, India

Received 4 June 2013; Accepted 8 July 2013

Academic Editors: P. Koshlukov and H. Li

Copyright © 2013 Jayprakash Ninu Chaudhari and Dipak Ravindra Bonde. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 is a split exact sequence of -semimodules and maximal -semimodule homomorphisms with is a strong subsemimodule of , then ”. Also, some results of commutative diagram of -semimodules and maximal -homomorphisms having exact rows are obtained.