Kodai Mathematical Journal

On ideals of rings of fractions and rings of polynomials

Yuan Ting Nai and Dongsheng Zhao

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 9 July 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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

Export citation