形式三角矩阵环上的n-Gorenstein投射模  

n-Gorenstein projective modules over formal triangular matrix rings

作　　者：牛韶花 杨刚[1] NIU Shao-hua;YANG Gang(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,Gansu,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2022年第10期44-49,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12161049);兰州交通大学“百名青年优秀人才培养计划”基金资助项目;甘肃省自然科学基金资助项目(21JR7RA295)。

摘　　要：设n是整数,T=(■)是形式三角矩阵环,其中A,B是环,U是左B右A双模,U是投射模,U的平坦维数有限。证明了若左T-模(M_(1)M_(2))_(φ^(M))是n-Gorenstein投射模,则M_(1)是(n-1)-Gorenstein投射左A-模,M_(2)/Im(φ^(M))是n-Gorenstein投射左B-模,并且φ^(M):U■_(A)M_(1)→M_(2)是单射。反过来,若M_(1)是n-Gorenstein投射左A-模,M_(2)/Im(φ^(M))是n-Gorenstein投射左B-模,并且φ^(M):U■_(A)M_(1)→M_(2)是单射,则左T-模(M_(1)M_(2))_(φ^(M))是n-Gorenstein投射模。Let n be an integer,T=(■)a formal triangular matrix ring,where A and B are rings and U is a(B,A)-bimodule,U is projective,Uhas finite flat dimension.It is proved that,if a left T-module (M_(1)M_(2))_(φ^(M))is n-Gorenstein projective,then Mis (n-1)-Gorenstein projective in A-Mod,M_(1)/Im(φ)is n-Gorenstein projective in B-Mod,and φ:U■M_(1)→M_(2)is a monomorphism.Conversely,if Mis n-Gorenstein projective in A-Mod,M_(2)/Im(φ)is n-Gorenstein projective in B-Mod,andφ:U?M→Mis a monomorphism,then the left T-module(M_(1)M_(2))_(φ^(M)) is n-Gorenstein projective.

关 键 词：n-Gorenstein投射模 形式三角矩阵环 伴随对 

分 类 号：O154.2[理学—数学]