Titlebook: Commutative Algebra through Exercises; Andrea Bandini,Patrizia Gianni,Enrico Sbarra Textbook 2024 The Editor(s) (if applicable) and The Au

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Kumudhini Akasapu,Ramagopal V. S. Uppaluri (→ p. 272) Prove that a partial order relation > is a well-order on . if and only if every descending chain in . is stationary.

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Agro and Food Processing Technologies (→p. 290) We say that a generating set of an .-module . is . if none of its proper subsets is still a generating set of ..

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Messaouda Benabdelkader,R. Saifi,H. Saifi (→ p. 319) Let . be a ring, and let ., ., and . be .-modules.

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Messaouda Benabdelkader,R. Saifi,H. Saifi (→ p. 345) Let . be a field, and let . be a .-vector space.

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RingsIn this chapter, we provide an introduction to the general theory of commutative rings with identity. We begin by reviewing fundamental concepts and properties related to such rings and their elements. We then proceed to discuss ring homomorphisms and homomorphism theorems, ideals and various operations commonly associated with them.

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