Abstract
As a proper generalization of comultiplication modules, the concept of k-comultipli-cation semimodules is introduced in this paper. Let S be a semiring. An left S-semimodule M is called a left k-comultiplication semimodule if for each subtractive subsemimodule N of M, there exists an ideal I of S such that . Some properties of k-comultiplication semimodules are obtained and some conditions are given for a direct sum of k-comultiplication semimodules to be a k-comultiplication semimodule.
2020 Mathematics Subject Classification: