余代数上的Gorenstein弱投射余模  

Gorenstein weak projective comodules over a coalgebra

作　　者：杨龙姣 姚海楼[1] YANG Longjiao;YAO Hailou(Department of Mathematics,Faculty of Science,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]北京工业大学理学部数学系,北京100124

出　　处：《山东大学学报（理学版）》2023年第8期43-47,56,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12071120)。

摘　　要：首先引入并研究余代数上的Gorenstein弱投射余模;其次利用推出图与左C-余模短正合列给出了弱投射性与Gorenstein弱投射性之间的关系,得到了一个余模是Gorenstein弱投射余模的等价刻画;最后引入n-Gorenstein弱投射余模,证明每个n-Gorenstein弱投射余模是Gorenstein弱投射余模以及若M是弱投射维数有限的n-Gorenstein弱投射余模,则M是弱投射余模等结论。The Gorenstein weak projective comodules over a coalgebra are introduced and studied.The relationships between weak projectivity and Gorenstein weak projectivity are obtained by using the push-out diagram and the short exact sequence of the left C-comodules.Meanwhile,an equivalent characterization is also obtained that a comodule is a Gorenstein weak projective comodule.Finally,n-Gorenstein weak projective comodules are intruoduced and proved that every n-Gorenstein weak projective comodule is a Gorenstein weak projective comodule,and if M is an n-Gorenstein weak projective comodule with finite projective dimension,then M is a weak projective comodule.

关 键 词：Gorenstein弱投射余模 Gorenstein弱投射维数 n-Gorenstein弱投射余模 

分 类 号：O153.3[理学—数学]