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Commutative Rings

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Part of the Graduate Texts in Mathematics book series (GTM,volume 242)

Commutative algebra, the study of commutative rings and related concepts, originated with Kummer’s and Dedekind’s study of the arithmetic properties of algebraic integers, and grew very quickly with the development of algebraic geometry, which consumes vast amounts of it. This chapter contains general properties of ring extensions, Noetherian rings, and prime ideals; takes a look at algebraic integers; and ends with a very minimal introduction to algebraic geometry.

Keywords

  • Prime Ideal
  • Maximal Ideal
  • Commutative Ring
  • Algebraic Variety
  • Galois Group

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-0-387-71568-1_7
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(2007). Commutative Rings. In: Abstract Algebra. Graduate Texts in Mathematics, vol 242. Springer, New York, NY. https://doi.org/10.1007/978-0-387-71568-1_7

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