Browse > Article
http://dx.doi.org/10.4134/BKMS.2014.51.2.579

Nil＊-COHERENT RINGS  

Xiang, Yueming (Department of Mathematics and Applied Mathematics Huaihua University)
Ouyang, Lunqun (Department of Mathematics Hunan University of Science and Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.2, 2014 , pp. 579-594 More about this Journal
Abstract
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;
Citations & Related Records
연도 인용수 순위
  • Reference
1 F.W. Anderson and K. R. Fuller, Rings and Categories of Modules, New York, Springer-Verlag, 1974.
2 S. U. Chase, Direct products of modules, Trans. Amer. Math. Soc. 97 (1960), 457-473.   DOI   ScienceOn
3 T. J. Cheatham and D. R. Stone, Flat and projective character modules, Proc. Amer. Math. Soc. 81 (1981), no. 2, 175-177.   DOI   ScienceOn
4 J. L. Chen and Y. Q. Zhou, Characterizations of coherent rings, Comm. Algebra 27 (2001), no. 5, 2491-2501.
5 N. Q. Ding, Y. L. Li, and L. X. Mao, J-coherent rings, J. Algebra Appl. 8 (2009), no. 2, 139-155.   DOI   ScienceOn
6 M. E. Harris, Some results on coherent rings, Proc. Amer. Math. Soc. 17 (1966), 474-479.   DOI   ScienceOn
7 S. Glaz, Commutative Coherent Rings, in: Lecture Notes in Math., 1371, Springer-Verlag, Berlin-Heidelberg-New York, 1989.
8 R. Gobel and J. Trlifaj, Approximations and Endomorphism Algebras of Modules, Berlin-New York, Walter de Gruyter, 2006.
9 H. Holm and P. Jorgensen, Covers, preenvelopes and purity, Illinois J. Math. 52 (2008), no. 2, 691-703.
10 T. Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematic, 189, Springer-Verlag, 1999.
11 T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematic, 131, Springer-Verlag, 2001.
12 L. X. Mao, Min-flat modules and min-coherent rings, Comm. Algebra 35 (2007), no. 2, 635-650.   DOI   ScienceOn
13 L. X. Mao, Weak global dimension of coherent rings, Comm. Algebra 35 (2007), no. 12, 4319-4327.   DOI   ScienceOn
14 L. X. Mao and N. Q. Ding, On divisible and torsionfree modules, Comm. Algebra 36 (2008), no. 2, 708-731.   DOI   ScienceOn
15 W. K. Nicholson and M. F. Yousif, Quasi-Frobenius Rings, Cambridge University Press, Cambridge, 2003.
16 K. Pinzon, Absolutely pure covers, Comm. Algebra 36 (2008), no. 6, 2186-2194.   DOI   ScienceOn
17 J. R. Garcia Rozas and B. Torrecillas, Relative injective covers, Comm. Algebra 22 (1994), no. 8, 2925-2940.   DOI   ScienceOn
18 J. Rada and M. Saorin, Rings characterized by (pre)envelopes and (pre)covers of their modules, Comm. Algebra 26 (1998), no. 3, 899-912.   DOI   ScienceOn
19 J. J. Rotman, An Introduction to Homological Algebra, Academic Press, New York, 1979.
20 F. L. Sandomierski, Homological dimensions under change of rings, Math. Z. 130 (1973), 55-65.   DOI
21 T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematic, 131, Springer-Verlag, 2001.
22 N. Q. Ding, On envelopes with the unique mapping property, Comm. Algebra 24 (1996), no. 4, 1459-1470.   DOI   ScienceOn
23 E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, Walter de Gruyter, Berlin, Now York, 2000.