形式三角矩阵环上的PGF模
PGF Modules over Formal Triangular Matrix Rings
DOI: 10.12677/PM.2020.1011130, PDF, HTML,    国家自然科学基金支持
作者: 薛淑娴, 杨 刚*：兰州交通大学数理学，甘肃 兰州
关键词: 形式三角矩阵环；PGF模；Formal Triangular Matrix Ring； PGF Module
摘要: 设是形式三角矩阵环，其中A,B是环，U是左B右A双模。证明了若BU的平坦维数有限，UA平坦维数或内射维数有限，则左是PGF模当且仅当左A-模M1是PGF模，左B-模M2/Im(φM)是PGF模，φM:U⊗AM1→M2是单射。
Abstract: Let be a formal triangular matrix ring, where A and B are rings and U is a (B, A)-bimodule. We prove that, if BU has finite flat dimension, and UA has finite flat or injective dimension, then a left is PGF if and only if M1 is  PGF in A-Mod, M2/Im(φM) is PGF in B-Mod and φM:U⊗AM1→M2 is a monomorphism.
文章引用：薛淑娴, 杨刚. 形式三角矩阵环上的PGF模[J]. 理论数学, 2020, 10(11): 1088-1096. https://doi.org/10.12677/PM.2020.1011130

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