三角矩阵环上的absolutely clean模与GorensteinAC-平坦模

doi:10.6040/j.issn.1671-9352.0.2020.200

Abstract

Abstract: Let T=(A 0U B) be a formal triangular matrix ring, where A and B are rings and U is a (B,A)-bimodule. In this article, we investigate absolutely clean T-modules and Gorenstein AC-flat T-modules. More specifically, under some mild conditions, we prove that L=(L1, L2) is absolutely clean right T-module then L1 is absolutely clean right A-module and L₂ is absolutely clean right B-module. As an application of this result, under some conditions, we show that M=(M1M2)_φ^M is Gorenstein AC flat left T-module if and only if M1 is a Gorenstein AC flat left A-module, M2/Im φ^M is a Gorenstein AC flat left B-module and the morphism φ^M is a monomorphism.

Key words: absolutely clean module, Gorenstein AC flat module, formal triangular matrix ring

CLC Number:

O153.3

DI Zhen-xing, LI Xiao-man. Absolutely clean modules and Gorenstein AC flat modules over formal triangular matrix rings[J].JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(12): 81-88.

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Absolutely clean modules and Gorenstein AC flat modules over formal triangular matrix rings

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