Nil-COHERENT RINGS

Title & Authors
Nil-COHERENT RINGS
Xiang, Yueming; Ouyang, Lunqun;

Abstract
Let R be a ring and $\small{Nil_*}$(R) be the prime radical of R. In this paper, we say that a ring R is left $\small{Nil_*}$-coherent if $\small{Nil_*}$(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 $\small{Nil_*}$-coherent rings are also studied in terms of N-injective modules and N-flat modules.
Keywords
$\small{Nil_*}$-coherent ring;strongly $\small{Nil_*}$-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
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.

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

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.

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

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.

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.

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

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

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.

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

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.

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.