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.
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© 2007 Springer Science+Business Media, LLC
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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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DOI: https://doi.org/10.1007/978-0-387-71568-1_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-71567-4
Online ISBN: 978-0-387-71568-1
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