Mathematische Nachrichten· 2026Q1
On Rings Whose Skew Generalized Power Series Rings Are Left Ikeda–Nakayama
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- 2026year
Short summary
This paper investigates when skew generalized power series rings (SGPSRs) built from a ring R and a partially ordered monoid M are left Ikeda–Nakayama (left IN) rings, continuing prior research.
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Key points
- Investigates the left Ikeda–Nakayama (left IN) property in skew generalized power series rings (SGPSRs).
- SGPSRs are constructed from a ring R and a strictly (or partially) ordered monoid M.
- Examines the relationship between the left IN property of R and the left IN property of the resulting SGPSR.
- Connects the left IN property to other ring-theoretic properties such as abelian, $\alpha$-Armendariz, and $\alpha$-McCoy rings.
AI-generated from the title and abstract; the full text is not read.
Abstract
ABSTRACT This paper continues our research on the Ikeda–Nakayama property (IN) in noncommutative ring constructions, building upon our previous works. Let be a ring, a strictly (or partially) ordered monoid, and a monoid homomorphism. The skew generalized power series ring consists of all functions from to whose support contains neither infinite descending chains nor infinite antichains, equipped with pointwise addition and multiplication defined by convolution twisted via the action of . Our study is closely connected to the question of whether a skew generalized power series ring over a left Ikeda–Nakayama ring is itself left Ikeda–Nakayama. This property is closely related to left self‐injective rings and provides insight into the characterization of such rings. We further examine their relationship with other important ring‐theoretic properties, such as being abelian, ‐Armendariz, and ‐McCoy.
The authors' abstract, as published at the source. Mathematische Nachrichten, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics