## Journal of the Mathematical Society of Japan

### A classification of graded extensions in a skew Laurent polynomial ring, II

#### Abstract

Let $V$ be a total valuation ring of a division ring $K$ with an automorphism $\sigma$ and let $A=\oplus_{i\in \mbi{Z}} A_{i} X^{i}$ be a graded extension of $V$ in $K[X,X^{-1};\sigma]$, the skew Laurent polynomial ring. We classify $A$ by distinguishing three different types based on the properties of $A_{1}$ and $A_{-1}$, and a complete description of $A_{i}$ for all $i\in \mbi{Z}$ is given in the case where $A_{1}$ is not a finitely generated left $O_{l}(A_{1})$-ideal.

#### Article information

Source
J. Math. Soc. Japan, Volume 61, Number 4 (2009), 1111-1130.

Dates
First available in Project Euclid: 6 November 2009

https://projecteuclid.org/euclid.jmsj/1257520502

Digital Object Identifier
doi:10.2969/jmsj/06141111

Mathematical Reviews number (MathSciNet)
MR2421983

Zentralblatt MATH identifier
1204.16031

Subjects
Primary: 16W50: Graded rings and modules

#### Citation

XIE, Guangming; MARUBAYASHI, Hidetoshi. A classification of graded extensions in a skew Laurent polynomial ring, II. J. Math. Soc. Japan 61 (2009), no. 4, 1111--1130. doi:10.2969/jmsj/06141111. https://projecteuclid.org/euclid.jmsj/1257520502

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