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S-Noetherian Modules and Rings

In: Chain Conditions in Commutative Rings

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  • Ali Benhissi

    (Faculty of Sciences of Monastir, Department of Mathematics)

Abstract

All the rings considered in this chapter are commutative with unity. If no contrary mention is expressed, all the multiplicative sets are supposed containing 1 and not containing 0. The results of the five first sections are due to Anderson and Dumitrescu (Comm Algebra 30(9), 4407–4416, 2002). Noetherian rings constitute an important tool in commutative algebra. For this reason, many mathematicians lock to generalize this notion in order to generalize known results for Noetherian rings. One possible generalization is S −Noetherian modules and rings, introduced and studied for the first time, by D.D. Anderson and T. Dumitrescu.

Suggested Citation

  • Ali Benhissi, 2022. "S-Noetherian Modules and Rings," Springer Books, in: Chain Conditions in Commutative Rings, chapter 0, pages 1-109, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-09898-7_1
    DOI: 10.1007/978-3-031-09898-7_1
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