Modules with fully invariant submodules essential in fully invariant summands

Communications in Algebra

Volumn 30, Issue 4, 2002, Pages 1833-1852

  Birkenmeier, Gary F ^a   Keol Park, Jae ^a   Tariq Rizvi, S ^a  

^a UNIVERSITY OF LOUISIANA AT LAFAYETTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036553685     PISSN: 00927872     EISSN: None     Source Type: Journal    
DOI: 10.1081/AGB-120013220     Document Type: Article

References (28)

1. Birkenmeier, G.F.; Müller, B.J.; Rizvi, S.T. Modules in which Every Fully Invariant Submodule is Essential in a Direct Summand. Comm. Algeb., To appear.
2. Birkenmeier, G.F.; Cǎlugǎreanu, G.; Fuchs, L; Goeters, H.P. The Fully-Invariant-Extending Property for Abelian Groups. Comm. Algeb. 2001, 29, 673-685.
3. Birkenmeier, G.F. A Generalization of FPF Rings. Comm. Algeb. 1989, 17, 855-884.
4. Birkenmeier, G.F.; Park, J.K.; Rizvi, S.T. Generalized Triangular Matrix Rings and the Fully Invariant Extending Property. Preprint.
5. Rizvi, S.T. Open Problems, The International Symposium on Ring Theory; Birkenmeier, G.F., Park, J.K., and Park, Y.S., Eds.; Trends in Math., Birkhäuser: Boston, 2001; 443-445.
6. Clark, W.E. Twisted Matrix Units Semigroup Algebras. Duke Math. J. 1967, 34, 417-424.
7. Kaplansky, I. Rings of Operators; Benjamin: New York, 1965.
8. Birkenmeier, G.F. Idempotents and Completely Semiprime Ideals. Comm. Algeb. 1983, 11, 567-590.
9. Wisbauer, R. Modules and Algebras: Bimodule Structure and Group Action on Algebras; Longman, 1996.
10. Birkenemier, G.F.; Heatherly, H.E.; Kim, J.Y.; Park, J.K. Triangular Matrix Representations. J. Algeb. 2000, 230, 558-595.
11. Birkenmeier, G.F.; Kim, J.Y.; Park, J.K. A Counterexample for CS-Rings. Glasgow Math. J. 2000, 42, 263-269.
12. Ferrero, M.; Wisbauer, R. Closure Operations in Module Categories. Algeb. Colloq. 1996, 3, 169-182.
13. Mohamed, S.; Müller, B.J. Continuous and Discrete Modules; Cambridge Univ. Press: Cambridge, 1990.
14. Chatters, A.W.; Hajarnavis, C.R. Rings with Chain Conditions; Pitman Press: London, 1980.
15. Okniński, J. Semigroup Algebras; Marcel Dekker: New York, 1991.
16. Passman, D.S. The Algebraic Structure of Group Rings; Wiley: New York, 1977.
17. Birkenmeier, G.F.; Park, J.K. Triangular Matrix Representations of Normalizing Extensions. Preprint.
18. Faith, C. Injective Quotient Rings of Commutative Rings, Module Theory; Springer Lecture Notes 1979, 700, Springer-Verlag: Berlin, 151-203.
19. Birkenmeier, G.F.; Kim, J.Y.; Park, J.K. When is the CS Condition Hereditary?. Comm. Algeb. 1999, 27, 3875-3885.
20. Birkenmeier, G.F. Decomposition of Baer-Like Rings. Acta Math. Hung. 1992, 59, 319-326.
21. Bell, H.E. Near-Rings in Which Each Element is a Power of Itself. Bull. Australian Math. Soc. 1970, 2, 363-368.
22. Vanaja, N. All Finitely Generated M-Subgenerated Modules are Extending. Comm. Algeb. 1996, 24, 543-572.
23. Müller, B.J.; Rizvi, S.T. Ring Decompositions of CS-Rings, Absracts for Methods in Module Theory Conference; Colorado Springs, May 1991.
24. Birkenmeier, G.F.; Tucci, R.P. Homomorphic Images and the Singular Ideal of a Strongly Right Bounded Ring. Comm. Algeb. 1988, 16, 1099-1112.
25. Dung, N.V.; Huynh, D.V.; Smith, P.F.; Wisbauer, R. Extending Modules; Longman: Burnt Mill, 1994.
26. Jategaonkar, A.V. Endomorphism Rings of Torsionless Modules. Trans. Amer. Math. Soc. 1971, 161, 457-466.
27. Chatters, A.W.; Khuri, S.M. Endomorphism Rings of Modules over Nonsingular CS Rings. J. London Math Soc. 1980, 21, 434-444.
28. Fuchs, L. Infinite Abelian Groups, II; Academic Press: New York, 1973.