Journal of Mathematical Sciences: Advances and Applications
Author's: Guangming Xie, Chunxia Liu and Zifen Hong
Pages: [1] - [12]
Received Date: June 15, 2024
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100122304
Let V be a total valuation ring of a skew field 
be the additive group of the rational numbers,
and 
be the group of automorphisms of K. Let
be a group homomorphism, 
be the skew group ring of 
over K, and 
be its quotient ring. Let 
and 
Consider the natural map 
from 
to K and set 
It is shown that 
is a total valuation ring of and it is characterized by 
and V. If V is an invariant
valuation ring, 
is classified into three types, in order to
study the structure of 
(the value group of 
total valuation ring, invariant valuation ring, value group.
