Gorenstein正则环、奇点范畴和Ding模

doi:10.12386/A2019sxxb0031

鏁板瀛︽姤鈥衡�� 2019, Vol. 62 鈥衡�� Issue (2): 331-344.DOI: 10.12386/A2019sxxb0031

鈥� 璁烘枃鈥� 涓婁竴绡� 涓嬩竴绡�

Gorenstein姝ｅ垯鐜�佸鐐硅寖鐣村拰Ding妯�

姹啗楣�¹, 鐙勬尟鍏�²

1. 瑗垮寳甯堣寖澶у缁忔祹瀛﹂櫌鍏板窞 730070;
2. 瑗垮寳甯堣寖澶у鏁板涓庣粺璁″闄� 鍏板窞 730070

鏀剁鏃ユ湡:2018-09-03 淇洖鏃ユ湡:2018-09-14 鍑虹増鏃ユ湡:2019-03-15 鍙戝竷鏃ユ湡:2019-03-15
浣滆�呯畝浠�:姹啗楣�,E-mail:wangjunpeng1218@163.com;鐙勬尟鍏�,E-mail:dizhenxing19841111@163.com
鍩洪噾璧勫姪:
鍥藉鑷劧绉戝鍩洪噾璧勫姪椤圭洰锛�11601433锛夛紱涓浗鍗氬＋鍚庤嚜鐒剁瀛﹀熀閲戣祫鍔╅」鐩紙2106M602945XB锛�

Gorenstein Regular Rings, Singularity Categories and Ding Modules

Jun Peng WANG¹, Zhen Xing DI²

1. Department of Economics, Northwest Normal University, Lanzhou 730070, P. R. China;
2. Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China

Received:2018-09-03 Revised:2018-09-14 Online:2019-03-15 Published:2019-03-15

鎽樿/Abstract

鎽樿锛�

鏈枃璇佹槑浜嗕换鎰忕幆鐨勬暣浣� Ding 鎶曞皠缁存暟鍜屾暣浣揇ing 鍐呭皠缁存暟涓�鑷达紝鐮旂┒浜嗗鐐硅寖鐣村拰鐩稿浜� Ding妯＄殑绋冲畾鑼冪暣闂寸殑鍏崇郴锛� 骞跺埢鐢讳簡 Gorenstein锛堟鍒欙級鐜互鍙婄幆鐨勬暣浣撶淮鏁扮殑鏈夐檺鎬�.

鍏抽敭璇�: Gorenstein 姝ｅ垯鐜�, Ding 鎶曞皠妯�, 濂囩偣鑼冪暣

Abstract:

We prove that the global Ding projective dimension and global Ding injective dimension coincide for any ring. We investigate the relationship between singularity categories and stable categories with respect to Ding modules, and characterize Gorenstein (regular) rings and the finiteness of left global dimension of rings in terms of singularity categories and Ding modules.

Key words: Gorenstein regular ring, Ding projective module, singularity category

涓浘鍒嗙被鍙�:

O154.2

姹啗楣�, 鐙勬尟鍏�. Gorenstein姝ｅ垯鐜�佸鐐硅寖鐣村拰Ding妯J]. 鏁板瀛︽姤, 2019, 62(2): 331-344.

Jun Peng WANG, Zhen Xing DI. Gorenstein Regular Rings, Singularity Categories and Ding Modules[J]. Acta Mathematica Sinica, Chinese Series, 2019, 62(2): 331-344.

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閾炬帴鏈枃: https://actamath.cjoe.ac.cn/Jwk_sxxb_cn/CN/10.12386/A2019sxxb0031

https://actamath.cjoe.ac.cn/Jwk_sxxb_cn/CN/Y2019/V62/I2/331

鍙傝�冩枃鐚�

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Gorenstein姝ｅ垯鐜�佸鐐硅寖鐣村拰Ding妯�

Gorenstein Regular Rings, Singularity Categories and Ding Modules

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