Titlebook: Chain Conditions in Commutative Rings; Ali Benhissi Textbook 2022 The Editor(s) (if applicable) and The Author(s), under exclusive license

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Concerto

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Encapsulate

https://doi.org/10.1007/978-3-031-09898-7S-Noetherian; S-Artinian; Nonnil-Noetherian; Strongly Hopfian; polynomials; power series; almost principal

鈍劍

978-3-031-10147-2The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

dragon

Tables 23 - 32, Figs. 90 - 114,ed in many areas including commutative algebra and algebraic geometry. The Noetherian property was originally due to the mathematician Noether who first considered a relation between the ascending chain condition on ideals and the finitely generatedness of ideals.

FIN

Tables 23 - 32, Figs. 90 - 114,domorphism . of ., the sequence . .???. ..??… is stationary. The ring . is strongly Hopfian if it is strongly Hopfian as an .-module. This is also equivalent to the fact that for each .?∈?., the sequence .(.)???.(..)??… is stationary. In this chapter, we study this notion and its transfer to differe

FIN

沖突

Nucleate

Tables 23 - 32, Figs. 90 - 114,In this chapter, all the rings considered are commutative with unity. A multiplicative set contains 1 and does not contain 0.

PAD416

1.0.3 List of symbols and abbreviations,Let . be an integral domain. In this chapter, we define a notion of almost principal for the domain .[.]. Then we characterize those . with this property. All the rings considered in this chapter are commutative with identity.