Let $V$ be a total valuation ring of a division ring $K$ with an automorphism $\sigma$ and let $A=\oplus _{i\in \bm{Z}} A_i X^{i}$ be a graded extension of $V$ in $ K[X,X^{-1};\sigma]$ , the skew Laurent polynomial ring. We classify $A$ by distinguishing four different types based on the properties of $A_1$ and $A_{-1}$ . A complete description of $A_{i}$ for all $i\in \bm{Z}$ is given in the case where $A_{1}$ is a finitely generated left $O_{l}(A_1)$ -ideal.
Publié le : 2008-04-15
Classification:
graded extension,
total valuation ring,
skew Laurent polynomial ring,
homogeneous element,
division ring,
16W50
@article{1212156657,
author = {XIE, Guangming and MARUBAYASHI, Hidetoshi},
title = {A classification of graded extensions in a skew Laurent polynomial ring},
journal = {J. Math. Soc. Japan},
volume = {60},
number = {1},
year = {2008},
pages = { 423-443},
language = {en},
url = {http://dml.mathdoc.fr/item/1212156657}
}
XIE, Guangming; MARUBAYASHI, Hidetoshi. A classification of graded extensions in a skew Laurent polynomial ring. J. Math. Soc. Japan, Tome 60 (2008) no. 1, pp. 423-443. http://gdmltest.u-ga.fr/item/1212156657/