Proceedings of the American Mathematical Society

Author(s): Ángel del Río; Juan Jacobo Simón
Journal: Proc. Amer. Math. Soc. 134 (2006), 1257-1263.
MSC (2000): Primary 16S50; Secondary 16P20, 16P40
Posted: October 4, 2005
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Abstract: For a unital ring

, RCFM $_\alpha (R)$ denotes the ring of row and column finite matrices over

indexed by $\alpha$ . We give necessary and sufficient structural conditions on RCFM $_\alpha(R)$ which are equivalent to

being, respectively, Quasi-Frobenius, left artinian, and left noetherian.

1.: G.D. Abrams, Morita equivalence for rings with local units, Comm. Algebra 11 (1983) 801-837. MR 0695890 (85b:16037)
2.: G. Abrams and J. Haefner, Picard groups and infinite matrix rings, Trans. Amer. Math. Soc. 350 (1998) 2737-2752. MR 1422591 (98j:16017)
3.: P.N. Ánh and L. Márki, Morita equivalence for rings without identity, Tsukuba J. Math. 11 (1987) 1-16. MR 0899719 (88h:16054)
4.: F.W. Anderson and K.R. Fuller, Rings and categories of modules, Springer-Verlag, 1974.MR 0417223 (54:5281)
5.: P. Ara, E. Pardo and F. Perera, The structure of countably generated projective modules over regular rings, J. Algebra 226 (2000) 161-190.MR 1749882 (2001a:16017)
6.: G.M. Brodskii, Endomorphism rings of free modules, Mat. Sb. 94(136) (1974) 226-242. Math. USSR Sbornik 23(2) (1974). MR 0349761 (50:2254)
7.: V. Camillo, F.J. Costa-Cano and J.J. Simón, Relating properties of a ring and its ring of row and column finite matrices, J. Algebra 224 (2001) 435-449. MR 1859035 (2002i:16039)
8.: C. Faith, Algebra II. Ring Theory, Springer-Verlag, 1976. MR 0427349 (55:383)
9.: P. Menal, On the endomorphism ring of a free module, Publ. Sec. Mat. Univ. Autònoma Barcelona 27 (1983), no. 1, 141-154. MR 0763863 (86g:16046)
10.: K.C. O'Meara, The exchange property for row and column-finite matrix rings, J. Algebra 268 (2003) no. 2, 744-749. MR 2009331 (2004i:16040)
11.: D. Ornstein, Dual vector spaces, Ann. Math. 69 (1959) 520-534.MR 0107153 (21:5878)
12.: B. L. Osofsky, Some properties of rings reflected in endomorphism rings of free modules, Cont. Math. 13 (1982), 179-181. MR 0685934 (84a:00007)
13.: R. Ware and J. Zelmanowitz, The Jacobson radical of the endomorphism ring of a projective module, Proc. AMS 26 (1970) 15-20.MR 0262281 (41:6891)

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 16S50, 16P20, 16P40

Ángel del Río
Affiliation: Departamento de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain
Email: adelrio@um.es

Juan Jacobo Simón
Affiliation: Departamento de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain
Email: jsimon@um.es

DOI: 10.1090/S0002-9939-05-08090-1
PII: S 0002-9939(05)08090-1
Received by editor(s): September 2, 2004
Received by editor(s) in revised form: November 19, 2004
Posted: October 4, 2005
Additional Notes: Both authors were partially supported by the D.G.I. of Spain and Fundación Séneca of Murcia
Communicated by: Martin Lorenz
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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