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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Noetherian and Artinian Rings. Primary DecompositionNoetherian, and that . is Artinian if and only if, up to isomorphism, it is a finite direct sum of local Artinian rings. This result generalizes what we have seen in Chapters 2 and 3, where A was a quotient of the polynomial ring ..

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Textbook 2024collection of 400 solved exercises, providing readers with the opportunity to apply theoretical knowledge to practical problem solving, fostering a deeper and more thorough understanding of the subject...The topics presented here are not commonly found in a single text. Consequently, the first part

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Commutative Algebra through Exercises978-3-031-56910-4Series ISSN 2038-5714 Series E-ISSN 2532-3318

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Mechanisation and Peasant AgricultureIn 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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Plasma Thermal and Nonthermal TechnologiesIn 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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