The rank condition and strong rank conditions for Ore extensions
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.
Fields of Study & Subjects
Rings
Modules
and Algebras
Advanced Topics in Algebra
Coding theory and cryptography
Publication details
- Journal / source
- Journal of Algebra and Its Applications
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 25
- Issue
- 09
- Publication date
- 27 February 2026
- Language
- EN