On graded-coherent like properties of commutative graded rings: a survey
Anass Assarrar and Najib Mahdou
Laboratory of Modeling and Mathematical Structures
Faculty of Science and Technology, Sidi Mohamed ben Abdellah University of Fez, Morocco
Pages 288–320 | Received 16 December 2023, Accepted 28 March 2024, Published 08 November 2024
Abstract
Let R be a commutative ring with nonzero identity and \Gamma (or sometimes G) a commutative monoid. The concept of coherent rings is one of the most significant notions in homological algebra. Because of its importance, there have been many generalizations to the notion of coherent rings. Some of them are linked the context of graded rings. In this paper, we survey known results concerning the different graded generalizations of coherent rings and modules.
Keywords: graded-Noetherian, graded-valuation domain, graded-valuation ring, graded Prüfer domains, graded-coherent, uniformly graded-coherent, graded-v-coherent, graded-quasi-coherent, graded-finite-conductor, graded-n-coherent, graded-S-coherent.
MSC numbers: Primary 13A15; Secondary 13A02.
Downloads: Full-text PDF