A domain R is called an absolutely S-domain (for short, AS-domain) if each domain T such that R ⊆ T ⊆ qf(R) is an S-domain. We show that R is an AS-domain if and only if for each valuation overring V of R and each height one prime ideal q of V, the extension R/(q ∩ R) ⊆ V/q is algebraic. A Noetherian domain R is an AS-domain if and only if dim (R) ≤ 1. In Section 2, we study a class of R-subalgebras of R[X] which share many spectral properties with the polynomial ring R[X] and which we call pseudo-polynomial rings. Section 3 is devoted to an affirmative answer to D. E. Dobbs's question of whether a survival pair must be a lying-over pair in the case of transcendental extension.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm94-1-1,
author = {Noomen Jarboui and Ihsen Yengui},
title = {Absolutely S-domains and pseudo-polynomial rings},
journal = {Colloquium Mathematicae},
volume = {91},
year = {2002},
pages = {1-19},
zbl = {1062.13500},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm94-1-1}
}
Noomen Jarboui; Ihsen Yengui. Absolutely S-domains and pseudo-polynomial rings. Colloquium Mathematicae, Tome 91 (2002) pp. 1-19. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm94-1-1/