投射余分解Gorenstein平坦复形

兰州理工大学学报 ›› 2020, Vol. 46 ›› Issue (6): 153-158.

投射余分解Gorenstein平坦复形

吴德军, 赵自红

兰州理工大学理学院, 甘肃兰州 730050

收稿日期:2019-09-18 出版日期:2020-12-28 发布日期:2021-01-07
作者简介:吴德军(1978-),男,甘肃金昌人,博士,副教授
基金资助:
国家自然科学基金(11761047)

Projectively coresolved Gorenstein flat complexes

WU De-jun, ZHAO Zi-hong

School of Science, Lanzhou Univ. of Tech., Lanzhou 730050, China

Received:2019-09-18 Online:2020-12-28 Published:2021-01-07

摘要/Abstract

摘要： 引入了投射余分解Gorenstein平坦复形的概念. 证明了对任意结合环R,G是投射余分解Gorenstein平坦复形当且仅当每个层次的R-模G^m是投射余分解Gorenstein平坦模, 其中∀m∈Z. 同时研究了投射余分解Gorenstein平坦复形的基本性质, 并探讨了复形G的投射余分解Gorenstein平坦维数与每个层次的R-模G^m的投射余分解Gorenstein平坦维数的关系.

关键词: PGF-复形, 预包络, 投射复形

Abstract: The concept of projectively coresolved Gorenstein flat complex is introduced. Over an arbitrary associate ring R, it is proven that G is a projectively coresolved Gorenstein flat complex if and only if each R-module G^m is a projective coresolved Gorenstein flat module for all m∈Z.Meanwhile, basic properties of projectively coresolved Gorenstein flat complexes are studied, and the relationship between projectively coresolved Gorenstein flat dimension of complex G and projectively coresolved Gorenstein flat dimension of each R-module G^m is discussed.

Key words: PGF-complex, preenvelope, projective complex

中图分类号:

O154.2

吴德军, 赵自红. 投射余分解Gorenstein平坦复形[J]. 兰州理工大学学报, 2020, 46(6): 153-158.

WU De-jun, ZHAO Zi-hong. Projectively coresolved Gorenstein flat complexes[J]. Journal of Lanzhou University of Technology, 2020, 46(6): 153-158.

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