Bull. Korean Math. Soc. 2014; 51(2): 579-594
Printed March 31, 2014
https://doi.org/10.4134/BKMS.2014.51.2.579
Copyright © The Korean Mathematical Society.
Yueming Xiang and Lunqun Ouyang
Huaihua University, Hunan University of Science and Technology
Let $R$ be a ring and $Nil_*(R)$ be the prime radical of $R$. In this paper, we say that a ring $R$ is left $Nil_*$-coherent if $Nil_*(R)$ is coherent as a left $R$-module. The concept is introduced as the generalization of left $J$-coherent rings and semiprime rings. Some properties of $Nil_*$-coherent rings are also studied in terms of $N$-injective modules and $N$-flat modules.
Keywords: $Nil_*$-coherent ring, strongly $Nil_*$-coherent ring, $N$-injective module, $N$-flat module, precover and preenvelope
MSC numbers: 16N60, 16E10, 16E05
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