TY  - JOUR
A1  - Gräter, Joachim
T1  - Free division rings of fractions of crossed products of groups with Conradian left-orders
JF  - Forum mathematicum
N2  - Let D be a division ring of fractions of a crossed product F[G, eta, alpha], where F is a skew field and G is a group with Conradian left-order <=. For D we introduce the notion of freeness with respect to <= and show that D is free in this sense if and only if D can canonically be embedded into the endomorphism ring of the right F-vector space F((G)) of all formal power series in G over F with respect to <=. From this we obtain that all division rings of fractions of F[G, eta, alpha] which are free with respect to at least one Conradian left-order of G are isomorphic and that they are free with respect to any Conradian left-order of G. Moreover, F[G, eta, alpha] possesses a division ring of fraction which is free in this sense if and only if the rational closure of F[G, eta, alpha] in the endomorphism ring of the corresponding right F-vector space F((G)) is a skew field.
KW  - crossed product
KW  - group ring
KW  - ordered group
KW  - Conradian left-order
KW  - locally indicable group
KW  - division ring of fractions
KW  - Hughes-free
KW  - formal
KW  - power series
Y1  - 2020
U6  - https://doi.org/10.1515/forum-2019-0264
SN  - 0933-7741
SN  - 1435-5337
VL  - 32
IS  - 3
SP  - 739
EP  - 772
PB  - De Gruyter
CY  - Berlin
ER  -