Y-Gorenstein内射模和Frobenius双模
Y-Gorenstein Injective Module and Frobenius Bimodules
DOI: 10.12677/PM.2021.115091, PDF, HTML, 下载: 498  浏览: 2,895  国家自然科学基金支持
作者: 王小妹：西北师范大学数学与统计学院, 甘肃 兰州
关键词: Y-Gorenstein 内射模；Frobenius 双模；生成子；Y-Gorenstein Injective Module； Frobenius Bimodules； Generator
摘要: 本文主要研究 Y-Gorenstein 内射模和 Frobenius 双模之间的关系. 设环 R 和 S 都是有单位元的结合环,SMR是 Frobenius 双模且MR是生成子.证明了 (1)Rop-模 X 是 Y-Gorenstein 内射模当且仅当 HomRop(M, X)是 Y-Gorenstein内射 Sop-模; (2) R-模 Y 是 Y-Gorenstein 内射模当且仅当 M ⊗RY 是 Y-Gorenstein 内射 S-模。
Abstract: In this paper, we mainly study the relationship between Y-Gorenstein injective module and Frobenius bimodules.  Let R and S be associative rings with an identity, SMR be Frobenius bimodule with MR a generator.  We proved that (1)  Rop -module X is  Y- Gorenstein injective module if and only if HomRop(M, X) is Y-Gorenstein injective Sop-module; (2) R -module Y is  Y-Gorenstein injective module if and only if  M ⊗RY is Y-Gorenstein injective S-module.
文章引用：王小妹. Y-Gorenstein内射模和Frobenius双模[J]. 理论数学, 2021, 11(5): 767-775. https://doi.org/10.12677/PM.2021.115091

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