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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).
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참고문헌 (15)
참고문헌 신청
E. Enochs / 1995 / Gorenstein injective and projective modules / Math. Z 220(4):611~633
E. Enochs / 1993 / Gorenstein flat modules / Nanjing Daxue Xuebao Shuxue Bannian Kan 10(1):1~9
Z. Gao / 2014 / All Gorenstein hereditary rings are coherent / J. Algebra Appl 13(4):5
B. G. Kang / 1989 / On the converse of a well-known fact about Krull domains / J. Algebra 124(2):284~299
I. Kaplansky / 1974 / Commutative Rings / Univ. Chicago Press
E. Enochs / 1993 / Gorenstein flat modules / Nanjing Daxue Xuebao Shuxue Bannian Kan 10(1):1~9
Z. Gao / 2014 / All Gorenstein hereditary rings are coherent / J. Algebra Appl 13(4):5
B. G. Kang / 1989 / On the converse of a well-known fact about Krull domains / J. Algebra 124(2):284~299
I. Kaplansky / 1974 / Commutative Rings / Univ. Chicago Press
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