On Partitioning and Subtractive Subsemimodules of Semimodules over Semirings
Jaiprakash Ninu Chaudhari, Dipak Ravindra Bond · Kyungpook mathematical journal · 2010
In this paper, we introduce a partitioning subsemimodule of a semimodule over a semiring which is useful to develop the quotient structure of semimodule.Indeed we prove : 1) The quotient semimodule M/N (Q) is essentially independent of choice of Q.3) Every partitioning subsemimodule is subtractive.4) Let N be a Q-subsemimodule of an R-semimodule M .Then A is a subtractive subsemimodule of M with N ⊆ A if and only if A/N (Q∩A) = {q + N : q ∈ Q ∩ A} is a subtractive subsemimodule of M/N (Q) .