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

@article{Daws2020RingtheoreticI,
title={Ring-theoretic (In)finiteness in reduced products of Banach algebras},
author={Matthew Daws and Bence Horv'ath},
year={2020},
volume={73},
pages={1423 - 1458}
}
• Published 2020
• Mathematics
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
3 Citations
Here collected are various updates, minor, and major corrections to papers. Mostly I am just correcting typos or adding references, but where major problems have occurred, I have added  to the title.
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