Strongly Hopfian, Endo-Noetherian, and Isonoetherian Rings

Ali Benhissi
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Ali Benhissi: Faculty of Sciences of Monastir, Department of Mathematics

Chapter Chapter 6 in Chain Conditions in Commutative Rings, 2022, pp 425-520 from Springer

Abstract: Abstract All rings considered in this chapter are commutative with identity. Let A be a ring and M a A-module. We say that M is strongly Hopfian if for each endomorphism f of M, the sequence ker f ⊆ ker f 2 ⊆… is stationary. The ring A is strongly Hopfian if it is strongly Hopfian as an A-module. This is also equivalent to the fact that for each a ∈ A, the sequence ann(a) ⊆ ann(a 2) ⊆… is stationary. In this chapter, we study this notion and its transfer to different extensions of a ring A.

Date: 2022
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DOI: 10.1007/978-3-031-09898-7_6

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