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Universal localization of triangular matrix rings

Author: Desmond Sheiham
Journal: Proc. Amer. Math. Soc. 134 (2006), 3465-3474
MSC (2000): Primary 13B30
Posted: June 12, 2006
MathSciNet review: 2240657
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Abstract: If is a triangular $2\times 2$ matrix ring, the columns and are f.g. projective -modules. We describe the universal localization of which makes invertible an -module morphism $\sigma:P\to Q$ , generalizing a theorem of A. Schofield. We also describe the universal localization of -modules.

References

1. P. Ara, M. A. González-Barroso, K. R. Goodearl, and E. Pardo.
Fractional skew monoid rings.
Journal of Algebra, 278(1):104-126, 2004. MR 2068068 (2005f:16042)
2. D. J. Benson.
Representations and cohomology. I. Basic Representation Theory of finite groups and associative algebras.
Cambridge Studies in Advanced Mathematics, 30. Cambridge University Press, 1995. MR 1110581 (92m:20005)
3. G. M. Bergman.
Modules over coproducts of rings.
Transactions of the American Mathematical Society, 200:1-32, 1974. MR 0357502 (50:9970)
4. G. M. Bergman.
Coproducts and some universal ring constructions.
Transactions of the American Mathematical Society, 200:33-88, 1974. MR 0357503 (50:9971)
5. G. M. Bergman and W. Dicks.
Universal derivations and universal ring constructions.
Pacific Journal of Mathematics, 79(2):293-337, 1978. MR 0531320 (81b:16024)
6. P. M. Cohn.
Localization in general rings, a historical survey.
Proceedings of the Conference on Noncommutative Localization in Algebra and Topology, ICMS, Edinburgh, 29-30 April, 2002, London Mathematical Society Lecture Notes 330, Cambridge University Press, 5-23, 2006.
7. P. M. Cohn.
Free Rings and their Relations.
London Mathematical Society Monographs, 2. Academic Press, London, 1971. MR 0371938 (51:8155)
8. P. M. Cohn.
Rings of fractions.
American Mathematical Monthly, 78:596-615, 1971. MR 0285561 (44:2779)
9. P. M. Cohn.
Free Rings and their Relations.
London Mathematical Society Monographs, 19. Academic Press, London, second edition, 1985. MR 0800091 (87e:16006)
10. P.M. Cohn and W. Dicks.
Localization in semifirs. II.
J. London Math.Soc. (2), 13(3):411-418, 1976. MR 0424856 (54:12814)
11. W. Dicks and E. Sontag.
Sylvester domains.
J. Pure Appl. Algebra, 13(3):243-275, 1978. MR 0509164 (80j:16014)
12. M. Farber and P. Vogel.
The Cohn localization of the free group ring.
Mathematical Proceedings of the Cambridge Philosophical Society, 111(3):433-443, 1992. MR 1151322 (93b:16049)
13. A. Haghany and K. Varadarajan.
Study of formal triangular matrix rings.
Communications in Algebra, 27(11):5507-5525, 1999. MR 1713049 (2000g:16003)
14. A. Haghany and K. Varadarajan.
Study of modules over formal triangular matrix rings.
Journal of Pure and Applied Algebra, 147(1):41-58, 2000. MR 1744654 (2000k:16004)
15. T. Y. Lam.
Lectures on Modules and Rings.
Number 189 in Graduate Texts in Mathematics. Springer, New York, 1999. MR 1653294 (99i:16001)
16. A. A. Ranicki.
Noncommutative localization in topology.
Proceedings of the Conference on Noncommutative Localization in Algebra and Topology, ICMS, Edinburgh, 29-30 April, 2002. arXiv:math.AT/0303046, London Mathematical Society Lecture Notes 330, Cambridge University Press, 81-102, 2006.
17. A. H. Schofield.
Representations of rings over skew fields, Volume 92 of London Mathematical Society Lecture Note Series.
Cambridge University Press, 1985. MR 0800853 (87c:16001)

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