Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Correspondences of closed submodules


Author: Julius M. Zelmanowitz
Journal: Proc. Amer. Math. Soc. 124 (1996), 2955-2960
MSC (1991): Primary 16S50; Secondary 16D70
DOI: https://doi.org/10.1090/S0002-9939-96-03469-7
MathSciNet review: 1342050
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $N$ is an $M$-faithful $R$-module, then there is an order-preserving correspondence between the closed $R$-submodules of $N$ and the closed $S$-submodules of $Hom_R(M,N)$, where $S=End_RM$.


References [Enhancements On Off] (What's this?)

  • 1. T. Albu and C. Nastasescu, Relative finiteness in module theory, Marcel Dekker, New York, 1984. MR 85k:16001
  • 2. A. W. Chatters and S. M. Khuri, Endomorphism rings of modules over non-singular $CS$-rings, J. London Math. Soc. (2) 21 (1980), 434--444. MR 82m:16033
  • 3. J. L. García Hernández and J. L. Gómez Pardo, Self-injective and PF endomorphism rings, Israel J. Math. 58 (1987), 324--350. MR 89b:16041
  • 4. J. L. García and M. Saorín, Endomorphism rings and category equivalences, J. Algebra 127 (1989), 182--205. MR 91b:16009
  • 5. J. L. Gómez Pardo, Endomorphism rings and dual modules, J. Algebra 130 (1990), 477--493. MR 91f:16040
  • 6. T. Kato, $U$-distinguished modules, J. Algebra 25 (1973), 15--24. MR 49:5100
  • 7. S. M. Khuri, Nonsingular retractable modules and their endomorphism rings, Bull. Austral. Math. Soc. 43 (1991), 63--71. MR 92b:16064
  • 8. Zhou Zhengping, Correspondence theorems for nondegenerate modules and their endomorphism rings, Proc. Amer. Math. Soc. 121 (1994), 25--32. MR 94g:16040
  • 9. J. M. Zelmanowitz, Representation of rings with faithful polyform modules, Comm. Algebra 14 (1986), 1141--1169. MR 87e:16078

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 16S50, 16D70

Retrieve articles in all journals with MSC (1991): 16S50, 16D70


Additional Information

Julius M. Zelmanowitz
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: julius@math.ucsb.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03469-7
Received by editor(s): March 7, 1995
Communicated by: Ken Goodearl
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society