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arXiv · 1904.07708

Injective Semimodules - Revisited

Jawad Abuhlail·Rangga Ganzar Noegraha
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Abstract

Injective modules play an important role in characterizing different classes of rings (e.g. Noetherian rings, semisimple rings). Some semirings have no non-zero injective semimodules (e.g. the semiring of non-negative integers). In this paper, we study some of the basic properties of the so called e-injective semimodules introduced by the first author using a new notion of exact sequences of semimodules. We clarify the relationships between the injective semimodules, the e-injective semimodule, and the i-injective semimodules through several implications, examples and counter examples. Moreover, we provide partial results for the so called Embedding Problem (of semimodules in injective semimodules).

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Jawad Abuhlail, Rangga Ganzar Noegraha. 2019-04-14. Injective Semimodules - Revisited. https://arxiv.org/abs/1904.07708

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