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Original Articles

On Uniform Diagonalisation of Matrices over Regular Rings and One-Accessible Regular Algebras

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Pages 3543-3562 | Received 01 Mar 2003, Published online: 01 Feb 2007

References

  • Amitsur , S. A. 1956 . Algebras over infinite fields . Proc. Am. Math. Soc. , 7 : 35 – 48 .
  • Amitsur , S. A. and Small , L. W. 1996 . Algebras over infinite fields, revisited . Israel J. Math. , 96 : 23 – 25 .
  • Ara , P. 1996 . Strongly π-regular rings have stable range one . Proc. Am. Math. Soc. , 124 : 3293 – 3298 .
  • Ara , P. , Goodearl , K. R. , O'Meara , K. C. and Pardo , E. 1997 . Diagonalisation of matrices over regular rings . Linear Algebra Appl. , 265 : 147 – 163 .
  • Ara , P. , Goodearl , K. R. , O'Meara , K. C. and Pardo , E. 1998 . Separative cancellation for projective modules over exchange rings . Israel J. Math. , 105 : 105 – 137 .
  • Ara , P. , Goodearl , K. R. , O'Meara , K. C. and Raphael , R. 2000 . K 1 of separative exchange rings and C*-algebras with real rank zero . Pacif. J. Math. , 195 : 261 – 275 .
  • Azumaya , G. 1954 . Strongly π-regular rings . J. Fac. Sci. Hokkaido Univ. I. , 13 : 34 – 39 .
  • Brookfield , G. 1998 . Direct sum cancellation of noetherian modules . J. Algebra , 200 : 207 – 224 .
  • De Meyer , F. and Ingraham , E. 1971 . Separable Algebras over Commutative Rings , Lecture Notes in Mathamatics. Berlin–Heidelberg–New York : Springer- Verlag .
  • Eklof , P. 1977 . “ Ultraproducts for algebraists ” . In Handbook of Mathematical Logic , Studies in Logic, 90 Edited by: Barwise , J. North-Holland .
  • Farkas , D. R. and Snider , R. L. 1981 . Locally finite-dimensional algebras . Proc. Am. Math. Soc. , 81 : 369 – 372 .
  • Fisher , J. L. 1971 . Embedding free algebras in skew fields . Proc. Am. Math. Soc. , 30 : 453 – 458 .
  • Goodearl , K. R. 1979 . Von Neumann Regular Rings , London: Pitman. 2nd Malabar, Fl : Krieger . 1991
  • Goodearl , K. R. , Menal , P. and Moncasi , J. 1993 . Free and residually artinian regular rings . J. Algebra , 156 : 407 – 432 .
  • Jacobson , N. 1980 . Basic Algebra II Freeman .
  • Lam , T. Y. 2001 . A First Course in Noncommutative Rings , 2nd Springer .
  • May , M. K. 1988 . A von Neumann regular ring that is locally finite, but not locally semisimple . Comm. Algebra , 16 : 103 – 113 .
  • Menal , P. 1994 . Collected Works Barcelona Societat Catalana de Matematiques, Filial de l′Institut d′Estudis Catalans, ISBN 84-7283-260-0
  • Olivier , J. P. 1968 . Anneaux absolument plats universels et épimorphismes d'anneaux . C.R. Acad. Sci. Paris, Série A , 266 : 317 – 318 .
  • O'Meara , K. C. and Raphael , R. M. 2001 . Uniform diagonalisation of matrices over regular rings . Algebra Universalis , 45 : 383 – 405 .
  • O'Meara , K. C. and Vinsonhaler , C. 1999 . Separative cancellation and multi- isomorphism in torsion-free abelian groups . J. Algebra , 221 : 536 – 550 .
  • Pardo , E. 1996 . Comparability, separativity, and exchange rings . Comm. Algebra , 24 : 2915 – 2929 .
  • Passman , D. S. 1971 . Infinite Group Rings New York : Marcel Dekker Inc .
  • Perera , F. 2000 . Lifting units modulo exchange ideals and C*-algebras with real rank zero . J. Reine Angew. Math. , 522 : 51 – 62 .
  • Pierce , R. S. 1967 . Modules over commutative regular rings . Memoirs Am. Math. Soc. , 70
  • Pierce , R. S. 1982 . Associative Algebras New York, Heidelberg, Berlin : Springer-Verlag .
  • Rowen , L. H. 1988 . Ring Theory Academic Press, Inc .
  • Yu , H. P. 1995 . On strongly π-regular rings of stable range one . Bull. Australian Math. Soc. , 51 : 433 – 437 .
  • Zariski , O. and Samuel , P. 1960 . Commutative Algebra. Volume II New York- Heidelberg-Berlin : Springer-Verlag .
  • #Communicated by A. Facchini.
  • Deceased in March 2004. At the suggestion of the first author we dedicate this paper to the late D.V. Tyukavkin.

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