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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ModulesIn this chapter we study modules over a ring A and their homomorphisms. We will highlight similarities and distinctions between modules and both Abelian groups and vector spaces, which serve as important examples when A = . and when A = K is a field, respectively.

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修正案

Rings and Ideals (! p. 245) Let . be a subset of a ring ...Prove that (.) is the intersection of all ideals of . containing ..

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COM

Modules (→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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Tensor Product (→ p. 319) Let . be a ring, and let ., ., and . be .-modules.

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Localization (→ p. 329) Let . be a finite ring, and let . . . be a multiplicative subset.

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Prosaic

True or False? (→ p. 357) Let . be a ring, and let . . . be an ideal. An element . . . is not a zero-divisor in . if and only if . : (.) = ..

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Review Exercises (→ p. 372) Let . be a ring such that every prime ideal is finitely generated.