Absolutely S-domains and pseudo-polynomial rings

• Autorzy: Noomen Jarboui , Ihsen Yengui
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 13C15: Dimension theory, depth, related rings (catenary, etc.)
• 13B25: Polynomials over commutative rings
• 13B02: Extension theory
• 13E05: Noetherian rings and modules
• 13A18: Valuations and their generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2002
• Tom: 94
• Numer: 1
• Strony: 1-19

Daty

wydano

2002

Twórcy

autor

Noomen Jarboui

• Department of Mathematics, Faculty of Sciences, University of Sfax, B.P. 802, 3018 Sfax, Tunisia

autor

Ihsen Yengui

• Department of Mathematics, Faculty of Sciences B.P. 802, 3018 Sfax, Tunisia, University of Sfax

Identyfikatory

DOI

10.4064/cm94-1-1