| 形式三角矩阵环上的n-Gorenstein投射模 |
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| 引用本文： | 牛韶花,杨刚.形式三角矩阵环上的n-Gorenstein投射模[J].山东大学学报(理学版),2022,57(10):44-49. |
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| 作者姓名： | 牛韶花 杨刚 |
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| 作者单位： | 兰州交通大学数理学院, 甘肃 兰州 730070 |
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| 基金项目： | 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) |
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| 摘 要： | 设n是整数,T=(A 0U B)是形式三角矩阵环,其中A,B是环,U是左B右A双模,BU是投射模,UA的平坦维数有限。证明了若左T-模(M1M2)φM是n-Gorenstein投射模,则M1是(n-1)-Gorenstein投射左A-模,M2/Im(φM)是n-Gorenstein投射左B-模,并且 φM:U?AM1→M2是单射。反过来,若M1是n-Gorenstein投射左A-模,M2/Im(φM)是n-Gorenstein投射左B-模,并且 φM:U?AM1→M2是单射,则左T-模(M1M2)φM是n-Gorenstein投射模。
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| 关 键 词： | n-Gorenstein投射模 形式三角矩阵环 伴随对 |
n-Gorenstein projective modules over formal triangular matrix rings |
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| NIU Shao-hua,YANG Gang.n-Gorenstein projective modules over formal triangular matrix rings[J].Journal of Shandong University,2022,57(10):44-49. |
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| Authors: | NIU Shao-hua YANG Gang |
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| Affiliation: | School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China |
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| Abstract: | Let n be an integer, T=(A 0U B) a formal triangular matrix ring, where A and B are rings and U is a (B,A)-bimodule, BU is projective, UA has finite flat dimension. It is proved that, if a left T-module (M1M2)φM is n-Gorenstein projective, then M1 is (n-1)-Gorenstein projective in A-Mod, M2/Im(φM)is n-Gorenstein projective in B-Mod, and φM:U?AM1→M2 is a monomorphism. Conversely, if M1 is n-Gorenstein projective in A-Mod, M2/Im(φM) is n-Gorenstein projective in B-Mod, and φM:U?AM1→M2 is a monomorphism, then the left T-module (M1M2)φM is n-Gorenstein projective. |
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| Keywords: | n-Gorenstein projective module formal triangular matrix ring adjoint pair |
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