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Noether Normalization

In: Emmy Noether in Bryn Mawr

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  • Judith D. Sally

    (Northwestern University, College of Arts and Sciences, Department of Mathematics)

Abstract

A remarkable fact about Emmy Noether’s work in commutative ring theory is that the foundation for the general theory of ideals which she laid in the 1920s remains today essentially as she laid it. It is an understatement to say it is well known that in an abstract commutative ring the ascending chain condition (acc) on ideals is equivalent to the existence of a finite basis for each ideal and that primary decomposition exists in an abstract commutative ring with acc on ideals. These ideas and many others found in Noether’s two most famous papers in commutative ring theory: “Idealtheorie in Ringbereichen” and “Abstrakter Aufbau der Idealtheorie in algebraischen Zahl-und Funktionenkörpern” were revolutionary in the 1920s but are very familiar today.

Suggested Citation

  • Judith D. Sally, 1983. "Noether Normalization," Springer Books, in: Bhama Srinivasan & Judith D. Sally (ed.), Emmy Noether in Bryn Mawr, pages 41-45, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-5547-5_3
    DOI: 10.1007/978-1-4612-5547-5_3
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