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Nil-COHERENT RINGS
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 Title & Authors
Nil-COHERENT RINGS
Xiang, Yueming; Ouyang, Lunqun;
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 Abstract
Let R be a ring and (R) be the prime radical of R. In this paper, we say that a ring R is left -coherent if (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 -coherent rings are also studied in terms of N-injective modules and N-flat modules.
 Keywords
-coherent ring;strongly -coherent ring;N-injective module;N-flat module;precover and preenvelope;
 Language
English
 Cited by
1.
Commutative rings and modules that are Nil*-coherent or special Nil*-coherent, Journal of Algebra and Its Applications, 2017, 16, 10, 1750187  crossref(new windwow)
 References
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. crossref(new window)

3.
T. J. Cheatham and D. R. Stone, Flat and projective character modules, Proc. Amer. Math. Soc. 81 (1981), no. 2, 175-177. crossref(new window)

4.
J. L. Chen and Y. Q. Zhou, Characterizations of coherent rings, Comm. Algebra 27 (2001), no. 5, 2491-2501.

5.
N. Q. Ding, On envelopes with the unique mapping property, Comm. Algebra 24 (1996), no. 4, 1459-1470. crossref(new window)

6.
N. Q. Ding, Y. L. Li, and L. X. Mao, J-coherent rings, J. Algebra Appl. 8 (2009), no. 2, 139-155. crossref(new window)

7.
E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, Walter de Gruyter, Berlin, Now York, 2000.

8.
S. Glaz, Commutative Coherent Rings, in: Lecture Notes in Math., 1371, Springer-Verlag, Berlin-Heidelberg-New York, 1989.

9.
R. Gobel and J. Trlifaj, Approximations and Endomorphism Algebras of Modules, Berlin-New York, Walter de Gruyter, 2006.

10.
M. E. Harris, Some results on coherent rings, Proc. Amer. Math. Soc. 17 (1966), 474-479. crossref(new window)

11.
H. Holm and P. Jorgensen, Covers, preenvelopes and purity, Illinois J. Math. 52 (2008), no. 2, 691-703.

12.
T. Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematic, 189, Springer-Verlag, 1999.

13.
T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematic, 131, Springer-Verlag, 2001.

14.
T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematic, 131, Springer-Verlag, 2001.

15.
L. X. Mao, Min-flat modules and min-coherent rings, Comm. Algebra 35 (2007), no. 2, 635-650. crossref(new window)

16.
L. X. Mao, Weak global dimension of coherent rings, Comm. Algebra 35 (2007), no. 12, 4319-4327. crossref(new window)

17.
L. X. Mao and N. Q. Ding, On divisible and torsionfree modules, Comm. Algebra 36 (2008), no. 2, 708-731. crossref(new window)

18.
W. K. Nicholson and M. F. Yousif, Quasi-Frobenius Rings, Cambridge University Press, Cambridge, 2003.

19.
K. Pinzon, Absolutely pure covers, Comm. Algebra 36 (2008), no. 6, 2186-2194. crossref(new window)

20.
J. R. Garcia Rozas and B. Torrecillas, Relative injective covers, Comm. Algebra 22 (1994), no. 8, 2925-2940. crossref(new window)

21.
J. Rada and M. Saorin, Rings characterized by (pre)envelopes and (pre)covers of their modules, Comm. Algebra 26 (1998), no. 3, 899-912. crossref(new window)

22.
J. J. Rotman, An Introduction to Homological Algebra, Academic Press, New York, 1979.

23.
F. L. Sandomierski, Homological dimensions under change of rings, Math. Z. 130 (1973), 55-65. crossref(new window)