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June 2015 On ideals of rings of fractions and rings of polynomials
Yuan Ting Nai, Dongsheng Zhao
Kodai Math. J. 38(2): 333-342 (June 2015). DOI: 10.2996/kmj/1436403894

Abstract

We investigate the links between the lattice Idl( R) of ideals of a commutative ring R and the lattices Idl( R′) of ideals of various new rings R′ constructed from R, in particular, the ring S −1 R of fractions and the ring R[ X] of polynomials. For any partially ordered set P, we construct another poset N( P) and show that P satisfies the ascending chain condition if and only if N( P) satisfies the ascending chain condition. As an application of this result, we give an order version proof for Hilbert's Basis Theorem.

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Yuan Ting Nai. Dongsheng Zhao. "On ideals of rings of fractions and rings of polynomials." Kodai Math. J. 38 (2) 333 - 342, June 2015. https://doi.org/10.2996/kmj/1436403894

Information

Published: June 2015
First available in Project Euclid: 9 July 2015

zbMATH: 1331.13002
MathSciNet: MR3368069
Digital Object Identifier: 10.2996/kmj/1436403894

Rights: Copyright © 2015 Tokyo Institute of Technology, Department of Mathematics

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Vol.38 • No. 2 • June 2015
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