| 形式三角矩阵环的Gorenstein遗传性和FP-内射性 |
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| 引用本文： | 闫美琪,姚海楼.形式三角矩阵环的Gorenstein遗传性和FP-内射性[J].数学研究及应用,2020,40(6):596-608. |
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| 作者姓名： | 闫美琪 姚海楼 |
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| 作者单位： | 北京工业大学理学部数学学院, 北京 100124 |
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| 基金项目： | 国家自然科学基金(Grant No.11671126) |
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| 摘 要： | 我们研究了形式三角矩阵环上模的Gorenstein(半遗传)遗传性,有限表现性和FP-内射性.给出了形式三角矩阵环是Gorenstein(半遗传)遗传的充要条件,并得出了形式三角矩阵环是n-FC环的充分条件.
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| 关 键 词： | Gorenstein (半遗传)遗传 形式三角矩阵环 FP-内射模 n-FC环 |
| 收稿时间： | 2019/11/19 0:00:00 |
| 修稿时间： | 2020/8/1 0:00:00 |
Gorenstein Hereditary and $FP$-Injectivity over Formal Triangular Matrix Rings |
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| Meiqi YAN,Hailou YAO.Gorenstein Hereditary and $FP$-Injectivity over Formal Triangular Matrix Rings[J].Journal of Mathematical Research with Applications,2020,40(6):596-608. |
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| Authors: | Meiqi YAN Hailou YAO |
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| Institution: | School of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, P. R. China |
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| Abstract: | In this paper we study Gorenstein (semiheredity) heredity, finite presentedness and $FP$-injectivity of modules over a formal triangular matrix ring. We provide necessary and sufficient conditions for such rings to be Gorenstein (semihereditary) hereditary and investigate when a triangular matrix ring is an $n$-$FC$ ring. |
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| Keywords: | Gorenstein (semihereditary) hereditary formal triangular matrix ring $FP$-injective module $n$-$FC$ ring |
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