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arXiv · 1303.3924

Semicorings and Semicomodules

Jawad Y. Abuhlail
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Abstract

In this paper, we introduce and investigate \emph{semicorings} over associative semirings and their categories of \emph{semicomodules.} Our results generalize old and recent results on corings over rings and their categories of comodules. The generalization is \emph{not} straightforward and even subtle at some places due to the nature of the base category of commutative monoids which is neither Abelian (not even additive) nor homological, and has no non-zero injective objects. To overcome these and other difficulties, a combination of methods and techniques from categorical, homological and universal algebra is used including a new notion of exact sequences of semimodules over semirings.

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Jawad Y. Abuhlail. 2013-03-15. Semicorings and Semicomodules. https://arxiv.org/abs/1303.3924

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