Properties of P-coherent and Baer modules

Springer Science and Business Media LLC - Tập 60 Số 2 - Trang 97-114 - 2010
Lixin Mao1
1Institute of Mathematics, Nanjing Institute of Technology, Nanjing, China

Tóm tắt

Từ khóa


Tài liệu tham khảo

F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer-Verlag, New York, 1974.

L. Angeleri-Hügel, Endocoherent modules, Pacific J. Math., 212 (2003), 1–11.

J. E. Björk, Rings satisfying certain chain conditions, J. Reine Angew. Math., 245 (1970), 63–73.

V. Camillo, Coherence for polynomial rings, J. Algebra, 132 (1990), 72–76.

R. Camps and W. Dicks, On semilocal rings, Israel J. Math., 81 (1993), 203–211.

N. V. Dung, D. V. Huyuh, P. F. Smith and R. Wisbauer, Extending Modules, Pitman, London, 1994.

E. E. Enochs, Injective and flat covers, envelopes and resolvents, Israel J. Math., 39 (1981), 189–209.

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

C. Faith, Embedding torsionless modules in projectives, Publ. Mat., 34 (1990), 379–387.

J. A. Fraser and W. K. Nicholson, Reduced PP-rings, Math. Japonica, 34 (1989), 715–725.

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

J. Jøndrup, p.p. rings and finitely generated flat ideals, Proc. Amer. Math. Soc., 28 (1971), 431–435.

M. A. Kamal and O. A. Elmnophy, On P-extending modules, Acta Math. Univ. Comenian., 74 (2005), 279–286.

T. Y. Lam, Lectures on Modules and Rings, Springer-Verlag, New York — Heidelberg — Berlin, 1999.

T. K. Lee and Y. Q. Zhou, Reduced modules, Rings, modules, algebras and abelian groups, Lecture Notes in Pure and Appl. Math. 236, Dekker, New York, 2004, 365–377.

L. X. Mao, A generalization of Noetherian rings, Taiwanese J. Math., 12 (2008), 501–512.

L. X. Mao, On P-coherent endomorphism rings, Proc. Indian Acad. Sci. Math. Sci., 118 (2008), 557–567.

L. X. Mao and N. Q. Ding, On divisible and torsionfree modules, Comm. Algebra, 36 (2008), 708–731.

L. X. Mao and N. Q. Ding, Notes on divisible and torsionfree modules, Comm. Algebra, 36 (2008), 4643–4658.

S. T. Rizvi and C. S. Roman, Baer and quasi-baer modules, Comm. Algebra, 32 (2004), 103–123.

S. T. Rizvi and C. S. Roman, On direct sums of Baer modules, J. Algebra, 321 (2009), 682–696.

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

R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia, 1991.

W. M. Xue, On PP rings, Kobe J. Math., 7 (1990), 77–80.

X. X. Zhang and J. L. Chen, A note on relative flatness and coherence, Comm. Algebra, 35 (2007), 3321–3330.