Generalized P-Flatness and P-Injectivity of Modules  ABSTRACT  |  FULL TEXT 

Year 2011, Volume: 40 Issue: 1, 27 - 40, 01.01.2011

Lixin Mao

Keywords

-

References

• Al-Ezeh, H. On generalized P F -rings. Math, J. Okayama Univ. 31, 25–29, 1989.
• Anderson, F. W. and Fuller, K. R. Rings and Categories of Modules (Springer-Verlag, New York, 1974).
• Bass, H. Finitistic dimension and a homological generalization of semiprimary rings, Trans. Amer. Math. Soc. 95, 466–488, 1960.
• Cheatham, T. J. and Stone, D. R. Flat and projective character modules, Proc. Amer. Math. Soc. 81 (2) 175–177, 1981.
• Colby, R. R. Rings which have flat injective modules, J. Algebra 35, 239–252, 1975.
• Dauns, J. and Fuchs, L. Torsion-freeness in rings with zero-divisors, J. Algebra Appl. 3, –237, 2004.
• Enochs, E. E. A note on absolutely pure modules, Canad. Math. Bull. 19, 361–362, 1976.
• Enochs, E. E. Flat covers and flat cotorsion modules, Proc. Amer. Math. Soc. 92, 179–184, Fuchs, L. and Salce, L. Modules over Non-Noetherian Domains (Math. Surveys and Mono- graphs. 84, Amer. Math. Soc., Providence, 2001).
• G¨obel, R. and Trlifaj, J. Approximations and Endomorphism Algebras of Modules (GEM , Walter de Gruyter, Berlin-New York, 2006).
• Goodearl, K. R. Ring Theory: Nonsingular Rings and Modules (Monographs Textbooks Pure Appl. Math. 33, Marcel Dekker Inc., New York and Basel, 1976).
• Hattori, A. A foundation of torsion theory for modules over general rings, Nagoya Math. J. 17, 147–158, 1960.
• Hirano, Y. On generalized PP-rings, Math. J. Okayama Univ. 25, 7–11, 1983.
• Huh, C., Kim, H. K. and Lee, Y. p.p. rings and generalized p.p. rings, J. Pure Appl. Algebra , 37–52, 2002.
• Jİndrup, J. p.p. rings and finitely generated flat ideals, Proc. Amer. Math. Soc. 28, 431–435, Jones, M. F. Coherence relative to a hereditary torsion theory, Comm. Algebra 10, 719–739, Kwak, T. K. Generalized Baer rings, Internat. J. Math. Math. Sci. ID 45837, 1–11, 2006.
• Lam, T. Y. Lectures on Modules and Rings (Springer-Verlag, New York, Heidelberg, Berlin, ). Mao L. X. On n-P -injective modules, College Math. 20 (1), 49–53, 2004 (in Chinese).
• Mao L. X. and Ding N. Q. On divisible and torsionfree modules, Comm. Algebra 36, 708– , 2008.
• Nam, S. B., Kim N. K. and Kim, J. Y. On simple GP-injective modules, Comm. Algebra (14), 5437–5444, 1995.
• Nicholson, W. K. On P P -rings, Period. Math. Hungarica 27 (2), 85–88, 1993.
• Nicholson, W. K. and Yousif, M. F. Principally injective rings, J. Algebra 174, 77–93, 1995. ˆOhori, M. On non-commutative generalized P.P . rings, Math. J. Okayama Univ. 26, 157– , 1984. ˆOhori, M. Some studies on generalized p.p. rings and hereditary rings, Math. J. Okayama Univ. 27, 53–70, 1985.
• Rotman, J. J. An Introduction to Homological Algebra (Academic Press, New York, 1979).
• Stenstr¨om, B. Coherent rings and F P -injective modules, J. London Math. Soc. 2, 323–329, Stenstr¨om, B. Rings of Quotients (Springer-Verlag, Berlin, Heidelberg, New York, 1975).
• Ware, R. Endomorphism rings of projective modules, Trans. Amer. Math. Soc. 155, 233– , 1971.
• Wisbauer, R. Foundations of Module and Ring Theory (Gordon and Breach, Philadelphia, ). Xue, W. M. On P P rings, Kobe J. Math. 7, 77–80, 1990.
• Yue Chi Ming, R. On von Neumann regular rings, Proc. Edinburgh Math. Soc. 19, 89–91, Yue Chi Ming, R. On annihilator ideals IV, Riv. Mat. Univ. Parma 13, 19–27, 1987.
• Yue Chi Ming, R. On p-injectivity and generalizations, Riv. Mat. Univ. Parma. 5 (5), 183– , 1996.
• Zhang, X. X., Chen, J. L. and Zhang, J. On (m, n)-injective modules and (m, n)-coherent rings, Algebra Colloq. 12, 149–160, 2005.
• Zhang, J. and Wu, J. Generalizations of principal injectivity, Algebra Colloq. 6, 277–282,