Ring-theoretic (In)finiteness in reduced products of Banach algebras

  title={Ring-theoretic (In)finiteness in reduced products of Banach algebras},
  author={Matthew Daws and Bence Horv'ath},
  journal={Canadian Journal of Mathematics},
  pages={1423 - 1458}
Abstract We study ring-theoretic (in)finiteness properties—such as Dedekind-finiteness and proper infiniteness—of ultraproducts (and more generally, reduced products) of Banach algebras. While we characterise when an ultraproduct has these ring-theoretic properties in terms of its underlying sequence of algebras, we find that, contrary to the $C^*$ -algebraic setting, it is not true in general that an ultraproduct has a ring-theoretic finiteness property if and only if “ultrafilter many” of… Expand
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