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.
Publié le : 2009-10-15
Classification:
graded extension,
total valuation ring,
skew Laurent polynomial ring,
homogeneous element,
division ring,
16W50
@article{1257520502,
author = {XIE, Guangming and MARUBAYASHI, Hidetoshi},
title = {A classification of graded extensions in a skew Laurent polynomial ring, II},
journal = {J. Math. Soc. Japan},
volume = {61},
number = {3},
year = {2009},
pages = { 1111-1130},
language = {en},
url = {http://dml.mathdoc.fr/item/1257520502}
}
XIE, Guangming; MARUBAYASHI, Hidetoshi. A classification of graded extensions in a skew Laurent polynomial ring, II. J. Math. Soc. Japan, Tome 61 (2009) no. 3, pp. 1111-1130. http://gdmltest.u-ga.fr/item/1257520502/