Gromov translation algebras over discrete trees are exchange rings |
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Authors: | P Ara K C O'Meara F Perera |
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Institution: | Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra (Barcelona), Spain ; Department of Mathematics, University of Canterbury, Christchurch, New Zealand ; Department of Pure Mathematics, Queen's University Belfast, Belfast, BT7 1NN, Northern Ireland |
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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 of matrices (over a field) of constant bandwidth. An extension of these ideas shows that for all real numbers in the unit interval , the growth algebras (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 in . |
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Keywords: | Translation algebra exchange ring von Neumann regular ring infinite matrices bandwidth dimension |
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