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Absolutely S-domains and pseudo-polynomial rings

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Jarboui N., Yengui I.

Colloquium Mathematicum

2002

tom 94

nr 1

1-19

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Jarboui N.

1 Yengui I.

1 2002

Wyniki wyszukiwania

Absolutely S-domains and pseudo-polynomial rings