Kodai Mathematical Journal

On ideals of rings of fractions and rings of polynomials

Yuan Ting Nai and Dongsheng Zhao

Full-text: Open access

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.

Article information

Source
Kodai Math. J., Volume 38, Number 2 (2015), 333-342.

Dates
First available in Project Euclid: 9 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1436403894

Digital Object Identifier
doi:10.2996/kmj/1436403894

Mathematical Reviews number (MathSciNet)
MR3368069

Zentralblatt MATH identifier
1331.13002

Citation

Nai, Yuan Ting; Zhao, Dongsheng. On ideals of rings of fractions and rings of polynomials. Kodai Math. J. 38 (2015), no. 2, 333--342. doi:10.2996/kmj/1436403894. https://projecteuclid.org/euclid.kmj/1436403894


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