Modules in which every fully invariant submodule is essential in a direct summand

Communications in Algebra

Volumn 30, Issue 3, 2002, Pages 1395-1415

  Birkenmeier, Gary F ^a   Müller, Bruno J ^a   Rizvi, S Tariq ^a  

^a UNIVERSITY OF LOUISIANA AT LAFAYETTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036013573     PISSN: 00927872     EISSN: None     Source Type: Journal    
DOI: 10.1081/AGB-120004878     Document Type: Article

References (27)

1. Dung, N.V.; Huynh, D.V.; Smith, P.F.; Wisbauer, R. Extending Modules; Longman: Burnt Mill, 1994.
2. Von Neumann, J. Continuous Geometries; Princeton Univ. Press: 1960.
3. Utumi, Y. On Continuous Rings and Selfinjective Rings. Trans. Amer. Math. Soc. 1965, 118, 158-173.
4. Birkenmeier, G.F. A Generalization of FPF Rings. Comm. Algeb. 1989, 17, 855-884.
5. Birkenmeier, G.F. Decomposition of Baer-Like Rings. Acta Math. Hungar. 1992, 59, 319-326.
6. Birkenmeier, G.F. When does a Supernilpotent Radical Essentially Split-Off?. J. Algebra 1995, 172, 49-60.
7. Müller, B.J.; Rizvi, S.T. Ring Decompositions of CS-Rings. in Abstracts for Methods in Module Theory Conference, May 1991; Colorado Springs.
8. Birkenmeier, G.F.; Cǎlugǎreanu, G.; Fuchs, L.; Goeters, H.P. The Fully-Invariant-Extension Property for Abelian Groups. Comm. Algeb. 2001, 29, 673-685.
9. Faith, C. The Maximal Regular Ideal of Self-Injective and Continuous Rings Splits Off. Arch. Math. 1985, 44, 511-521.
10. Clark, W.E. Twisted Matrix Units Semigroup Algebras. Duke Math. J. 1967, 34, 417-423.
11. Kaplansky, I. Rings of Operators; Mathematics Lecture Note Series; W.A. Benjamin: New York, 1968.
12. Chatters, A.W.; Khuri, S.M.; Endomorphism Rings of Modules Over Non-Singular CS Rings. J. London Math. Soc. 1980, 21, 434-444.
13. Birkenmeier, G.F. Idempotents and Completely Semiprime Ideals. Comm. Algeb. 1983, 11, 567-580.
14. Rotman, J.J. An Introduction to the Theory of Groups (3rd ed.); Wm. C. Brown: Dubuque, 1988.
15. Jeremy, L. Modules et Anneaux Quasi-Continus. Canad. Math. Bull. 1974, 17, 217-228.
16. Nicholson, W.K. Semiregular Modules and Rings. Can. J. Math. 1976, 28, 1105-1120.
17. Rowen, L. Ring Theory, Vol. I; Academic Press: Boston, 1988.
18. Müller, B.J. Problem 1. Ring Theory. Jain, S.K., Rizvi, S.T., Eds.; World Scientific, 1993.
19. Birkenmeier, G.F.; Kim, J.Y.; Park, J.K.; Quasi-Baer Ring Extensions and Biregular Rings. Bull. Austral. Math. Soc. 2000, 61, 39-52.
20. Goodearl, K.R. Ring Theory: Nonsingular Rings and Modules; Pure and Applied Mathematics Series 33; Marcel Dekker: New York, 1976.
21. Abulkheir, H.E.; Birkenmeier, G.F. Right Complement Bounded Semiprime Rings. Acta Math. Hungar. 1996, 70, 227-235.
22. Yue Chi Ming, R. Annihilators and Strongly Regular Rings. Rend. Sem. Fac. Sci. Univ. Cagliari 1987, 57, 51-59.
23. Birkenmeier, G.F. Baer Rings and Quasi-Continuous Rings Have a MDSN. Pacific J. Math. 1981, 97, 283-292.
24. Brown, K.A. The Singular Ideals of Group Rings. Quart. J. Math. Oxford 1977 28, 41-60.
25. Faith, C. Injective Quotient Rings of Commutative Rings. In Module Theory; Lecture Notes in Math, 700, Springer-Verlag: Heidelberg-New York, 1979; 151-203.
26. Mohamed, S.H.; Müller, B.J. Continuous and Discrete Modules; London Math. Soc. Lecture Note Series 147; Cambridge University Press: 1990.
27. Birkenmeier, G.F.; Tucci, R.P. Homomorphic Images and the Singular Ideal of a Strongly Right Bounded Ring, Comm. Algeb. 1988, 16, 1099-1112: Corrigenda 2661-2662.