Publisher : Department of Mathematics, Kyungpook National University
DOI : 10.5666/KMJ.2010.50.2.329
Title & Authors
On Partitioning and Subtractive Subsemimodules of Semimodules over Semirings Chaudhari, Jaiprakash Ninu; Bond, Dipak Ravindra;
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. 2) If f : M M' is a maximal R-semimodule homomorphism, then . 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 if and only if is a subtractive subsemimodule of .