关于C-无挠模和C-自反模的若干同调性质

doi:10.6040/j.issn.1671-9352.0.2018.105

《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (4): 72-79.doi: 10.6040/j.issn.1671-9352.0.2018.105

关于C-无挠模和C-自反模的若干同调性质

罗肖强¹,谭玲玲^2*,邢建民³

1.四川文理学院数学学院, 四川达州 635000;2.曲阜师范大学数学科学学院, 山东曲阜 273165;3.青岛科技大学数理学院, 山东青岛 266061

发布日期:2019-04-08
作者简介:罗肖强(1965— ), 男, 硕士, 副教授, 研究方向为半群与同调代数. E-mail:lxq1128@163.com*通信作者简介:谭玲玲(1986— ),女,硕士,讲师,研究方向为同调代数. E-mail:tanll@qfnu.edu.cn
基金资助:
四川省教育厅自然科学基金项目(17ZB0375)

On homological properties of C-torsionless and C-reflexive modules

LUO Xiao-qiang¹, TAN Ling-ling^2*, XING Jian-min³

1. Department of Mathematics, Sichuan University of Arts and Science, Dazhou 635000, Sichuan, China;
2. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China;
3. School of Mathematic and Physics, Qingdao University of Science and Technology, Qingdao 266061, Shandong, China

Published:2019-04-08

摘要/Abstract

摘要： 研究了关于半对偶化模的无挠和自反模的相对概念和同调性质。证明了当C是1-对偶化模时,投射模的子模是完全C-自反模,并且刻画了有有限G_C-维数的C-无挠和C-自反模类。此外还研究了模的G_C-维数与左C-正交维数的关系以及给出了C-自反包络存在的某些充分条件。

关键词: C-无挠模, C-自反模, 完全C-自反模, 半对偶化模, C-自反包络

Abstract: The relative notions and homological properties of torsionless and reflexive modules with respect to a semidualizing module are investigated. If C is a 1-dualizing module, then each submodule of a projective module is totally C-reflexive, and then the characterizations of C-torsionless and C-reflexive modules with finite G_C-dimension are investigated. Moreover, the relations between the G_C-dimension and the left C-orthogonal dimension of a module are studied, and some sufficient conditionson the existence of C-reflexive envelope are given.

Key words: C-torsionless module, C-reflexive module, totally C-reflexive module, semidualizing module, C-reflexive envelope

中图分类号:

O154.2

罗肖强,谭玲玲,邢建民. 关于C-无挠模和C-自反模的若干同调性质[J]. 《山东大学学报(理学版)》, 2019, 54(4): 72-79.

LUO Xiao-qiang, TAN Ling-ling, XING Jian-min. On homological properties of C-torsionless and C-reflexive modules[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(4): 72-79.

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关于C-无挠模和C-自反模的若干同调性质

On homological properties of C-torsionless and C-reflexive modules

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