On K-nonsingular modules and applications

Communications in Algebra

Volumn 35, Issue 9, 2007, Pages 2960-2982

  Rizvi, S Tariq ^a   Roman, Cosmin S ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

Baer modules; Continuous modules; Endomorphism rings; Extending modules; Nonsingular modules; Type theory decomposition

Indexed keywords

EID: 34748898965     PISSN: 00927872     EISSN: 15324125     Source Type: Journal    
DOI: 10.1080/00927870701404374     Document Type: Article

References (22)

1. Berberian, S. K. (1972). Baer *-Rings. Berlin-Heidelberg-New York: Springer-Verlag.
2. Birkenmeier, G. F., Kim, J. Y., Park, J. K. (2000). A counterexample for CS-rings. Glasgow Math. J. 42:263-269.
3. Birkenmeier, G. F., Heatherly, H. E., Kim, J. Y., Park, J. K. (2000). Triangular matrix representations. J. Algebra 230:558-595.
4. Birkenmeier, G. F., Park, J. K. (2003). Triangular matrix representations of ring extensions. J. Algebra 265:457-477.
5. Dung, N. V., Huynh, D. V., Smith, P. F., Wisbauer, R. (1994). Extending Modules. Harlow: Longman Scientific & Technical.
6. Goodearl, K. R. (1991). Von Neumann Regular Rings. Malabar: Robert E. Krieger Publishing Co., Inc.
7. Goodearl, K. R., Boyle, A. K. (1976). Dimension theory for nonsingular injective modules. Memoirs of the American Mathematical Society 7(177).
8. Kaplansky, I. (1968). Rings of Operators. New York: W. A. Benjamin.
9. Khuri, S. M. (1980). Endomorphism rings of nonsingular modules. Ann. Sc. Math. Québec IV(2):145-152.
10. Khuri, S. M. (1991). Nonsingular retractable modules and their endomorphism rings. Bull. Austral. Math. Soc. 43:63-71.
11. Khuri, S. M. (2004). Endomorphism Rings of Modules. Manuscript.
12. Kim, J. Y., Park, J. K. (1997). When is a regular ring a semisimple artinian ring? Math. Japonica 45(2):311-313.
13. Mewborn, A. C. (1971). Regular rings and Baer rings. Math. Z. 121:211-219.
14. Mohamed, S. H., Müller, B. J. (1990). Continuous and Discrete Modules. Cambridge: Cambridge University Press.
15. Müller, B. J., Rizvi, S. T. (1983). On injective and quasi-continuous modules. J. Pure Appl. Algebra 28(2):197-210.
16. Rizvi, S. T. (1988). Commutative rings for which every continuous module is quasi-injective. Arch. Math. 50(5):435-442.
17. Rizvi, S. T., Roman, C. S. (2004). Baer and quasi-Baer modules. Comm. Alg. 32(1):103-123.
18. Rizvi, S. T., Roman, C. S. (2005). Baer property of modules and applications. In: Chen, J. L., Ding, N. Q., Marubayashi, H., eds. Advances in Ring Theory. World Scientific, pp. 225-241.
19. Roman, C. S. (2004). Baer and Quasi-Baer Modules. Doctoral Dissertation, The Ohio State University.
20. Stenström, B. (1975). Rings of Quotients. Berlin-Heidelberg-New York: Springer Verlag.
21. Wisbauer, R. (1996). Modules and Algebras: Bimodule Structure and Group Actions on Algebras. Harlow: Longman.
22. Wolfson, KG. (1961). Baer rings of endomorphisms. Math. Annalen 143:19-28.