Year: 2026
Type: article
Abstract: Let [Formula: see text] be a ring, [Formula: see text] a ring endomorphism, and [Formula: see text] a [Formula: see text]-derivation. We establish that the Ore extension [Formula: see text] satisfies the rank condition if and only if [Formula: see text] does. In addition, we prove analogous results for the right and left strong rank conditions. However, in the right case, the “if” part requires the hypothesis that [Formula: see text] is an automorphism, whereas, in the left case, this assumption is needed for the “only if” part. Finally, we provide a new proof of an old result of Susan Montgomery stating that a skew power series ring is directly (respectively, stably) finite if and only if its coefficient ring is directly (respectively, stably) finite.
Authors: Karl Lorensen, Johan Öinert
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415036656
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