The Development of Non-Noetherian Grade and Its Applications
Hochster and Barger were the first to introduce notions of grade for non-Noetherian rings. Their work laid the foundation for Alfonsi’s work which unified and generalized these earlier definitions. The various notions of grade have played an important role in the development of the theory of coherent rings. This paper looks at the historical development of non-Noetherian grade, as well as its applications.
KeywordsNon-Noetherian ring Coherent ring Grade Depth Polynomial grade
Mathematics Subject Classification (2010):13-02 13C15 13D05
The author would like to thank the referee for their thorough reading and helpful comments to improve this paper. In addition, the author thanks Sarah Glaz for her suggestion regarding the need for the current work, as well as for her assistance and continued encouragement.
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