K-comultiplication semimodules

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 $N=(0{:}_M^{r}I)$. 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.

Keywords:

• Comultiplication module
• direct sum
• semimodule
• subtractive subsemimodule

2020 Mathematics Subject Classification:

• Primary: 16Y60
• Secondary: 16D99

Additional information

Funding

The first author is supported by National Natural Science Foundation of China (No. 11861043). The third author is supported by National Natural Science Foundation of China (No. 11761047).