Dual Rickart Modules

Communications in Algebra

Volumn 39, Issue 11, 2011, Pages 4036-4058

  Lee, Gangyong ^a,c   Rizvi, S Tariq ^b   Roman, Cosmin S ^b  

^a OHIO STATE UNIVERSITY   (United States)

^b OHIO STATE UNIVERSITY   (United States)

^c AL IMAM MOHAMMAD IBN SAUD ISLAMIC UNIVERSITY IMSIU   (Saudi Arabia)

Author keywords

Dual Baer modules; Endomorphism rings; Idempotents and annihilator; Rickart and Baer rings and modules; von Neumann regular rings

Indexed keywords

EID: 84857985272     PISSN: 00927872     EISSN: 15324125     Source Type: Journal    
DOI: 10.1080/00927872.2010.515639     Document Type: Article

References (36)

1. Armendariz, E. P. (1974). A note on extensions of Baer and P.P.-rings. J. Austral. Math. Soc. 18: 470 - 473.
2. Bergman, G. M. (1971). Hereditary commutative rings and centres of hereditary rings. Proc. London Math. Soc. 23 (3): 214 - 236.
3. Birkenmeier, G. F., Kim, J. Y., Park, J. K. (2000). Quasi-Baer ring extensions and biregular rings. Bull. Austral. Math. Soc. 61: 39 - 52.
4. Birkenmeier, G. F., Kim, J. Y., Park, J. K. (2001). Polynomial extensions of Baer and quasi-Baer rings. J. Pure Appl. Algebra 159: 25 - 42.
5. Birkenmeier, G. F., Kim, J. Y., Park, J. K. (2001). Principally quasi-Baer rings. Comm. Algebra 29 (2): 638 - 660.
6. Birkenmeier, G. F., Park, J. K. (2003). Triangular matrix representations of ring extensions. J. Algebra 265 (2): 457 - 477.
7. Camps, R., Dicks, W. (1993). On semilocal rings. Israel J. Math. 81: 203 - 211.
8. Clark, W. E. (1967). Twisted matrix units semigroup algebras. Duke Math. J. 34: 417 - 423.
9. Endo, S. (1960). Note on P.P. rings. Nagoya Math. J. 17: 167 - 170.
10. Evans, M. W. (1972). On commutative P.P. rings. Pacific J. Math. 41 (3): 687 - 697.
11. García Hernández, J. L. (1989). Properties of direct summands of modules. Comm. Algebra 17 (1): 73 - 92.
12. Goodearl, K. R. (1991/1979). Von Neumann Regular Rings., 2nd ed. London: Pitman, Krieger.
13. Hattori, A. (1960). A foundation of torsion theory for modules over general rings. Nagoya Math. J. 17: 147 - 158.
14. Jøndrup, S. (1971). P.P. rings and finitely generated flat ideals. Proc. Amer. Math. Soc. 28 (2): 431 - 435.
15. Kaplansky, I. (1968). Rings of operators. New York-Amsterdam: W. A. Benjamin Inc.
16. Khuri, S. M. (1978). Baer endomorphism rings and closure operators. Canad. J. Math.30(5):1070-1078.
17. Lam, T. Y. (1999). Lectures on Modules and Rings, GTM 189. Berlin-Heidelberg-New York: Springer Verlag.
18. Liu, Q., Ouyang, B. Y. (2006). Rickart modules. Nanjing Daxue Xuebao Shuxue Bannian Kan 23 (1): 157 - 166 (in Chinese).
19. Liu, Q., Ouyang, B. Y., Wu, T. S. (2009). Principally quasi-Baer modules. J. Math. Res. Exposition 29 (5): 823 - 830.
20. Lee, G., Rizvi, S. T., Roman, C. S. (2010). Rickart Modules. Comm. Algebra 38: 4005 - 4027.
21. Lee, G., Rizvi, S. T., Roman, C. S. Direct sums of Rickart modules. Manuscript, submitted.
22. Mohamed, S. H., Müller, B. J. (1990). Continuous and Discrete Modules. London Math. Soc. Lecture Note Ser. No. 147, Cambridge University Press.
23. Maeda, S. (1960). On a ring whose principal right ideals generated by idempotents form a lattice. J. Sci. Hiroshima Univ. Ser. A 24: 509 - 525.
24. Rangaswamy, K. M. (1967). Abelian groups with endomorphic images of special types. J. Algebra 6: 271 - 280.
25. Rizvi, S. T., Roman, C. S. (2004). Baer and quasi-Baer modules. Comm. Algebra 32 (1): 103 - 123.
26. Rizvi, S. T., Roman, C. S. (2005). Baer property of modules and applications. Advances in Ring Theory 225 - 241.
27. Rizvi, S. T., Roman, C. S. (2007). On K-nonsingular modules and applications. Comm. Algebra 35: 2960 - 2982.
28. Rizvi, S. T., Roman, C. S. (2009). On direct sums of Baer modules. J. Algebra 321 (2): 682 - 696.
29. Small, L. W. (1967). Semihereditary rings. Bull. Amer. Math. Soc. 73: 656 - 658.
30. Smith, P. F. (2005). Modules with many homomorphisms. J. Pure Appl. Algebra 197: 305 - 321.
31. Tsukerman, G. M. (1966). Rings of endomorphisms of free modules. Sibirsk. Mat. Zh. 7 (7): 1161 - 1167.
32. Tütüncü, D. K., Tribak, R. (2009). On T-noncosingular modules. Bull. Aust. Math. Soc. 80 (3): 462 - 471.
33. Tütüncü, D. K., Tribak, R. (2010). On dual Baer module. Glasg. Math. J. 52 (2): 261 - 269.
34. Ware, R. (1971). Endomorphism rings of projective modules. Trans. Amer. Math. Soc. 155: 233 - 256.
35. Ware, R., Zelmanowitz, J. (1970). Simple endomorphism rings. Amer. Math. Monthly 77 (9): 987 - 989.
36. Zelmanowitz, J. (1972). Regular modules. Trans. Amer. Math. Soc. 163: 340 - 355.