Gorenstein范畴上的一个问题

doi:10.12386/A2019sxxb0012

鏁板瀛︽姤鈥衡�� 2019, Vol. 62 鈥衡�� Issue (1): 151-156.DOI: 10.12386/A2019sxxb0012

鈥� 璁烘枃鈥� 涓婁竴绡� 涓嬩竴绡�

Gorenstein鑼冪暣涓婄殑涓�涓棶棰�

寮犱笢涓�¹, 鏈辨捣鐕�², 鑳℃睙鑳�³

1. 娴欐睙甯堣寖澶у鏁扮悊涓庝俊鎭伐绋嬪闄� 閲戝崕 321004;
2. 娴欐睙宸ヤ笟澶у鐞嗗闄� 鏉窞 310023;
3. 姹熻嫃鐞嗗伐瀛﹂櫌鏁扮悊瀛﹂櫌甯稿窞 321001

鏀剁鏃ユ湡:2018-01-29 淇洖鏃ユ湡:2018-03-08 鍙戝竷鏃ユ湡:2019-05-15
閫氳浣滆��: 鏈辨捣鐕�,E-mail:hyzhu@zjut.edu.cn
浣滆�呯畝浠�:寮犱笢涓�,E-mail:zdd@zjnu.cn;鑳℃睙鑳�,E-mail:jiangshenghu@jsut.edu.cn
鍩洪噾璧勫姪:
鍥藉鑷劧绉戝鍩洪噾锛�11501257锛�11671069锛�11771212锛夛紱涓浗鍗氬＋鍚庣瀛﹀熀閲戯紙2016M600426锛夛紱娴欐睙鐪佽嚜鐒剁瀛﹀熀閲戯紙LY18A010032锛夛紱涓浗鐣欏鍩洪噾濮旇祫鍔╅」鐩紱姹熻嫃楂樻牎“闈掕摑宸ョ▼”璧勫姪椤圭洰

On a Question of Gorenstein Categories

Dong Dong ZHANG¹, Hai Yan ZHU², Jiang Sheng HU³

1. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, P. R. China;
2. College of Science, Zhejiang University of Technology Hangzhou 310023, P. R. China;
3. School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 321001, P. R. China

Received:2018-01-29 Revised:2018-03-08 Published:2019-05-15

鎽樿/Abstract

鎽樿锛�

璁�A鏄樋璐濆皵鑼冪暣锛�X鏄�A鐨勫瓙鑼冪暣.Sather-Wagstaff锛孲harif鍜學hite寮曞叆浜咷orenstein瀛愯寖鐣寸殑姒傚康锛岃涓�G锛�X锛�.鎴戜滑鐢�PP锛堢浉搴斿湴锛�P锛変唬琛ㄧ函鎶曞皠R-妯＄被锛堢浉搴斿湴锛屾姇灏�R-妯＄被锛�.鏈枃缁欏嚭浜嗕竴绫绘弧瓒虫潯浠�“G锛�P锛�⊆G锛�PP锛�”鐨勭幆锛岀敱姝ょ粰鍑轰簡褰�W鏄�X鐨勫瓙鑼冪暣鏃讹紝G锛�W锛夋槸鍚﹀寘鍚湪G锛�X锛変腑鐨勪竴涓惁瀹氬洖绛�.杩涗竴姝ワ紝鍒荤敾浜嗗寘鍚叧绯�G锛�P锛�⊆G锛�PP锛夊拰G锛�PP锛�⊆G锛�P锛変綍鏃舵垚绔�.

鍏抽敭璇�: 绾姇灏勬ā, Gorenstein鎶曞皠妯�, Gorenstein鑼冪暣

Abstract:

Let A be an abelian category and X a subcategory of A. Sather-Wagstaff, Sharif and White introduced the Gorenstein subcategory G (X). Denote by PP the class of pure-projective R-modules and by P the class of projective R-modules. We show that there are some rings such that G (P) ⊆ G(PP), which gives a negative answer to the Question that whether G (W) is contained in G (X) provided that W is a subcategory of X. In addition, we give some characterizations of when G (P) ⊆ G (PP) and G (PP) ⊆ G (P) hold.

Key words: pure-projective module, Gorenstein projective module, Gorenstein category

涓浘鍒嗙被鍙�:

寮犱笢涓�, 鏈辨捣鐕�, 鑳℃睙鑳�. Gorenstein鑼冪暣涓婄殑涓�涓棶棰榌J]. 鏁板瀛︽姤, 2019, 62(1): 151-156.

Dong Dong ZHANG, Hai Yan ZHU, Jiang Sheng HU. On a Question of Gorenstein Categories[J]. Acta Mathematica Sinica, Chinese Series, 2019, 62(1): 151-156.

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閾炬帴鏈枃: https://actamath.cjoe.ac.cn/Jwk_sxxb_cn/CN/10.12386/A2019sxxb0012

https://actamath.cjoe.ac.cn/Jwk_sxxb_cn/CN/Y2019/V62/I1/151

鍙傝�冩枃鐚�

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Gorenstein鑼冪暣涓婄殑涓�涓棶棰�

On a Question of Gorenstein Categories

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