Some Studies Of Cancellative Semimodules And Well-Semimodules

In this dissertation we mainly investigate cancellative semimodules and well-semimodules.The module of difference of cancellative semimodules and its' homomorphism extention,tensor product of semimodules and semisimple decomposition of well-semimodules are studied.The dissertation falls into three parts.In the first section, we study homomorphism extention of cancellative semimodules and obtain module construction which is isomorphic to the module ofdifference of cancellative semimodules.Moreover ,a useful functor [-] is obtained.In the second section,we generalize semisimple decomposition of modules to semisimple decompositions of well-semimodules.In the last, we introduce a new kind of tensor product of semimodules,and prove two results.Let R is a semiring, M is a right R -semimodule, N is a lift R -semimodule,T is a N -semimodule,then exist N -semimodule isomorphicfrom Hom(M(?)_RN,T) to Hom_R(M,Hom(N,T));Also we show that right R -semimodule B is R -flat semimodule if and if for any left ideal I of R,exist N -ismorphic from B(?)_RI→BI.