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The Development of Non-Noetherian Grade and Its Applications

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Commutative Algebra

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. University of Indianapolis, 1400 East Hanna Avenue, Indianapolis, IN, 46227, USA

    Livia Hummel

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  1. Livia Hummel
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Correspondence to Livia Hummel .

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Editors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi Roma Tre, Rome, Italy

    Marco Fontana

  2. Department of Mathematics, Graz University of Technology, Graz, Austria

    Sophie Frisch

  3. Department of Mathematics, University of Connecticut, Storrs, Connecticut, USA

    Sarah Glaz

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Hummel, L. (2014). The Development of Non-Noetherian Grade and Its Applications. In: Fontana, M., Frisch, S., Glaz, S. (eds) Commutative Algebra. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0925-4_11

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