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A note on Gorenstein Pr\"ufer domains

Fanggui Wang|Longyu Xu|Kui Hu
대한수학회 (The Korean Mathematical Society)|2016.09|대한수학회보 (Bulletin of the KMS)|제53권 제5호|pp. 1447-1455

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키워드

PIDGorenstein projective moduleGorenstein Pr\"ufer domaincoherent ringUFD
주제분류수학

초록

In this note, we mainly discuss the Gorenstein Pr\"ufer domains. It is shown that a domain is a Gorenstein Pr\"ufer domain if and only if every finitely generated ideal is Gorenstein projective. It is also shown that a domain is a PID (resp., Dedekind domain, B\'ezout domain) if and only if it is a Gorenstein Pr\"ufer UFD (resp., Krull domain, GCD domain).

Abstract

In this note, we mainly discuss the Gorenstein Pr\"ufer domains. It is shown that a domain is a Gorenstein Pr\"ufer domain if and only if every finitely generated ideal is Gorenstein projective. It is also shown that a domain is a PID (resp., Dedekind domain, B\'ezout domain) if and only if it is a Gorenstein Pr\"ufer UFD (resp., Krull domain, GCD domain).

참고문헌 (15)

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