Absolutely S-domains and pseudo-polynomial rings

Noomen Jarboui, and Ihsen Yengui. "Absolutely S-domains and pseudo-polynomial rings." Colloquium Mathematicae 94.1 (2002): 1-19. <http://eudml.org/doc/285065>.

@article{NoomenJarboui2002,
abstract = {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.},
author = {Noomen Jarboui, Ihsen Yengui},
journal = {Colloquium Mathematicae},
keywords = {polynomial ring; Jaffard ring; survival extension; lying-over extension; absolutely S-domain; survival pair; lying-over pair},
language = {eng},
number = {1},
pages = {1-19},
title = {Absolutely S-domains and pseudo-polynomial rings},
url = {http://eudml.org/doc/285065},
volume = {94},
year = {2002},
}

TY - JOUR
AU - Noomen Jarboui
AU - Ihsen Yengui
TI - Absolutely S-domains and pseudo-polynomial rings
JO - Colloquium Mathematicae
PY - 2002
VL - 94
IS - 1
SP - 1
EP - 19
AB - 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.
LA - eng
KW - polynomial ring; Jaffard ring; survival extension; lying-over extension; absolutely S-domain; survival pair; lying-over pair
UR - http://eudml.org/doc/285065
ER -