Gorenstein Prüfer整环的一些新刻画

doi:10.12386/A2020sxxb0002

鏁板瀛︽姤鈥衡�� 2020, Vol. 63 鈥衡�� Issue (1): 19-26.DOI: 10.12386/A2020sxxb0002

鈥� 璁烘枃鈥� 涓婁竴绡� 涓嬩竴绡�

Gorenstein Prüfer鏁寸幆鐨勪竴浜涙柊鍒荤敾

鐔婃稕

瑗垮崕甯堣寖澶у鏁板涓庝俊鎭闄� 鍗楀厖 637002

鏀剁鏃ユ湡:2018-12-20 淇洖鏃ユ湡:2019-05-08 鍑虹増鏃ユ湡:2020-01-15 鍙戝竷鏃ユ湡:2020-01-15
浣滆�呯畝浠�:鐔婃稕,E-mail:Taoxiong2004@163.com
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Some Characterizations of Gorenstein Prüfer Domains

Tao XIONG

College of Mathematics and Information, China West Normal University, Nanchong 637002, P. R. China

Received:2018-12-20 Revised:2019-05-08 Online:2020-01-15 Published:2020-01-15

鎽樿/Abstract

鎽樿锛�

璁�R鏄暣鐜�.浼楁墍鍛ㄧ煡锛�R鏄疨rüfer鏁寸幆褰撲笖浠呭綋姣忎釜鍙櫎妯℃槸FP-鍐呭皠妯″綋涓斾粎褰撴瘡涓�h-鍙櫎妯℃槸FP-鍐呭皠妯�.鏈枃寮曡繘浜嗕竴绉嶆柊鐨凣orensteinFP-鍐呭皠妯★紝骞朵笖璇佹槑浜�R鏄疓orenstein Prüfer鏁寸幆褰撲笖浠呭綋姣忎釜鍙櫎妯℃槸Gorenstein FP-鍐呭皠妯★紝褰撲笖浠呭綋姣忎釜h-鍙櫎妯℃槸GorensteinFP-鍐呭皠妯�.

鍏抽敭璇�: Gorenstein FP-鍐呭皠妯�, Gorenstein Prü, fer鏁寸幆, 鍙櫎妯�, h-鍙櫎妯�

Abstract:

It is well known that a domain R is a Prüfer domain if and only if every divisible module is FP-injective; if and only if every h-divisible module is FP-injective. In this paper, we introduce the concept of Gorenstein FP-injective modules, and show that a domain R is a Gorenstein Prüfer domain if and only if every divisible module is Gorenstein FP-injective; if and only if every h-divisible module is Gorenstein FPinjective.

Key words: Gorenstein FP-injective modules, Gorenstein Prüfer Domains, divisible modules, h-divisible modules

涓浘鍒嗙被鍙�:

O153.3
O154

鐔婃稕. Gorenstein Prüfer鏁寸幆鐨勪竴浜涙柊鍒荤敾[J]. 鏁板瀛︽姤, 2020, 63(1): 19-26.

Tao XIONG. Some Characterizations of Gorenstein Prüfer Domains[J]. Acta Mathematica Sinica, Chinese Series, 2020, 63(1): 19-26.

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閾炬帴鏈枃: https://actamath.cjoe.ac.cn/Jwk_sxxb_cn/CN/10.12386/A2020sxxb0002

https://actamath.cjoe.ac.cn/Jwk_sxxb_cn/CN/Y2020/V63/I1/19

鍙傝�冩枃鐚�

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Gorenstein Prüfer鏁寸幆鐨勪竴浜涙柊鍒荤敾

Some Characterizations of Gorenstein Prüfer Domains

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