Abstract
In this paper, we introduce and investigate semicorings over associative semirings and their categories of semicomodules. Our results generalize old and recent ones on corings over rings and their categories of comodules. The generalization is not straightforward and even subtle at several places due to the nature of the base category of commutative monoids which is neither Abelian (not even additive) nor homological, and has no nonzero 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.
| Original language | English |
|---|---|
| Pages (from-to) | 4801-4838 |
| Number of pages | 38 |
| Journal | Communications in Algebra |
| Volume | 42 |
| Issue number | 11 |
| DOIs | |
| State | Published - Nov 2014 |
Bibliographical note
Funding Information:The author would like to acknowledge the support provided by the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum & Minerals (KFUPM) for funding this work through project No. IN080400.
Keywords
- Semicoalgebras
- Semicomodules
- Semicorings
- Semimodules
- Semirings
ASJC Scopus subject areas
- Algebra and Number Theory
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