On Exact Sequence of Semimodules over Semirings. (30th July 2013) - Chaudhari, Jayprakash Ninu; Bonde, Dipak Ravindra
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.