Gromov translation algebras over discrete trees are exchange rings

P. Ara, K. C. O'Meara, F. Perera

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8 Citations (Scopus)

Abstract

It is shown that the Gromov translation ring of a discrete tree over a von Neumann regular ring is an exchange ring. This provides a new source of exchange rings, including, for example, the algebras G(0) of ω × ω matrices (over a field) of constant bandwidth. An extension of these ideas shows that for all real numbers r in the unit interval, the growth algebras G(r) (introduced by Hannah and O'Meara in 1993) are exchange rings. Consequently, over a countable field, countable-dimensional exchange algebras can take any prescribed bandwidth dimension r in [0,1].
Original languageEnglish
Pages (from-to)2067-2079
JournalTransactions of the American Mathematical Society
Volume356
DOIs
Publication statusPublished - 1 May 2004

Keywords

  • Bandwidth dimension
  • Exchange ring
  • Infinite matrices
  • Translation algebra
  • Von Neumann regular ring

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    Ara, P., O'Meara, K. C., & Perera, F. (2004). Gromov translation algebras over discrete trees are exchange rings. Transactions of the American Mathematical Society, 356, 2067-2079. https://doi.org/10.1090/S0002-9947-03-03372-5