Year 2007,
Volume: 2 Issue: 2, 71 - 82, 01.12.2007
Abstract
It is proved that if R is a right and left Noetherian ring then the right R-module RI satisfies the ascending chain condition on n-generated submodules, for every positive integer n.
References
- M. E. Antunes Sim˜oes and P. F. Smith, Direct products satisfying the as- cending chain condition for submodules with a bounded number of generators, Comm. Algebra 23 (1995), 3525-3540.
- M. E. Antunes Sim˜oes and P. F. Smith, On the ascending chain condition for submodules with a bounded number of generators, Comm. Algebra 24 (1996), 1721.
- M. E. Antunes Sim˜oes and P. F. Smith, Rings whose free modules satisfy the ascending chain condition on submodules with a bounded number of genera- tors, J. Pure Appl. Algebra 123 (1998), 51-66.
- B. Baumslag and G. Baumslag, On ascending chain conditions, Proc. London Math. Soc. (3) 22 (1971), 681-704.
- P. M. Cohn, Free Rings and their Relations, Academic Press, London, 1971.
- D. Frohn, A counterexample concerning ACCP in power series rings, Comm. Algebra 30 (2002), 2961-2966.
- D. Frohn, Modules with n-acc and acc on certain types of annihilators, J. Algebra 256 (2002), 467-483.
- L. Fuchs, Infinite Abelian Groups Vols I, II, Academic Press, New York, 1970.
- K.R Goodearl and R. B. WarŞeld, Jr., An Introduction to Noncommutative Noetherian Rings, London Math. Soc. Student Texts 16, Cambridge Univ. Press, Cambridge, 1989.
- W. Heinzer and D. Lantz, Commutative rings with ACC on n-generated ideals, J. Algebra 80 (1983), 261-278.
- J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, Wiley- Interscience, Chichester, 1987.
- A.M. Nicolas, Sur les modules tels que toute suite croissante de sous-modules engendr´es par n g´en´erateurs soit stationnaire, J. Algebra 60 (1979), 249-260.
- G. Renault, Sur des conditions de chaines ascendantes dans des modules libres, J. Algebra 47 (1977), 268-275.
- G. Sabbach and P. Eklof, DeŞnability problems for modules and rings, J. Symbolic Logic 36 (1971), 623-649.
- B. Stenstr¨om, Rings of Quotients, Springer-Verlag, Berlin, 1975. Patrick F. Smith
- Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland UK E-mail: pfs@maths.gla.ac.uk
Year 2007,
Volume: 2 Issue: 2, 71 - 82, 01.12.2007
Abstract
References
- M. E. Antunes Sim˜oes and P. F. Smith, Direct products satisfying the as- cending chain condition for submodules with a bounded number of generators, Comm. Algebra 23 (1995), 3525-3540.
- M. E. Antunes Sim˜oes and P. F. Smith, On the ascending chain condition for submodules with a bounded number of generators, Comm. Algebra 24 (1996), 1721.
- M. E. Antunes Sim˜oes and P. F. Smith, Rings whose free modules satisfy the ascending chain condition on submodules with a bounded number of genera- tors, J. Pure Appl. Algebra 123 (1998), 51-66.
- B. Baumslag and G. Baumslag, On ascending chain conditions, Proc. London Math. Soc. (3) 22 (1971), 681-704.
- P. M. Cohn, Free Rings and their Relations, Academic Press, London, 1971.
- D. Frohn, A counterexample concerning ACCP in power series rings, Comm. Algebra 30 (2002), 2961-2966.
- D. Frohn, Modules with n-acc and acc on certain types of annihilators, J. Algebra 256 (2002), 467-483.
- L. Fuchs, Infinite Abelian Groups Vols I, II, Academic Press, New York, 1970.
- K.R Goodearl and R. B. WarŞeld, Jr., An Introduction to Noncommutative Noetherian Rings, London Math. Soc. Student Texts 16, Cambridge Univ. Press, Cambridge, 1989.
- W. Heinzer and D. Lantz, Commutative rings with ACC on n-generated ideals, J. Algebra 80 (1983), 261-278.
- J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, Wiley- Interscience, Chichester, 1987.
- A.M. Nicolas, Sur les modules tels que toute suite croissante de sous-modules engendr´es par n g´en´erateurs soit stationnaire, J. Algebra 60 (1979), 249-260.
- G. Renault, Sur des conditions de chaines ascendantes dans des modules libres, J. Algebra 47 (1977), 268-275.
- G. Sabbach and P. Eklof, DeŞnability problems for modules and rings, J. Symbolic Logic 36 (1971), 623-649.
- B. Stenstr¨om, Rings of Quotients, Springer-Verlag, Berlin, 1975. Patrick F. Smith
- Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland UK E-mail: pfs@maths.gla.ac.uk
There are 16 citations in total.
Details
| Other ID | JA79GH35RZ |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | December 1, 2007 |
| Published in Issue | Year 2007 Volume: 2 Issue: 2 |