# Absolutely S-domains and pseudo-polynomial rings

Colloquium Mathematicae (2002)

- Volume: 94, Issue: 1, page 1-19
- ISSN: 0010-1354

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topNoomen 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 -

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