Gromov translation algebras over discrete trees are exchange rings

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

Sortida de recercaRecercarevisió per companys

8 Cites (Scopus)


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].
Idioma originalEnglish
Pàgines (de-a)2067-2079
RevistaTransactions of the American Mathematical Society
Estat de la publicacióPublicada - 1 de maig 2004

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