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ON SMALL SUBTRACTIVE AND PROJECTIVE SEMIMODULES OVER ZERO-SUM SEMIRING
Keywords:
subtractive semimodule, zero-sum semiring, coclosed subsemimodule, amply supplemented, T-semimodule, relative projectivity, small M-a-projectivityAbstract
Many notions in modules theory have different generalizations in the theory of semimodules.
In the first part to this paper, we study coclosed and subtractive subsemimodules and obtain some proprieties of T-semimodules.
In the second part, we introduce the notion of small M-a-projective semimodules and characterize them in the category of subtractive semimodules over zero-sum semirings.
Received: September 7, 2022
Revised: December 24, 2022
Accepted: March 10, 2023
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