# 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}, journal={Canadian Journal of Mathematics}, year={2020}, volume={73}, 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

#### 3 Citations

Corrections and updates to papers

- 2020

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.

A purely infinite Cuntz-like Banach $*$-algebra with no purely infinite ultrapowers

- Mathematics
- 2021

We continue our investigation, from [7], of the ring-theoretic infiniteness properties of ultrapowers of Banach algebras, studying in this paper the notion of being purely infinite. It is well known… Expand

Perturbations of surjective homomorphisms between algebras of operators on Banach spaces

- Mathematics
- 2020

A remarkable result of Moln\'ar [Proc. Amer. Math. Soc., 126 (1998), 853-861] states that automorphisms of the algebra of operators acting on a separable Hilbert space is stable under ``small''… Expand

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