TY - THES
AU - Lee, Kit-sum
PY - 1978
TI - Topics on noncommutative localization and group rings
KW - Thesis/Dissertation
LA - eng
M3 - Text
AB - Three topics in localization theory and group ring theory are investigated.
In Chapter I, it is proved that every symmetric kernel functor in a left Noetherian ring is induced by a prime ideal. A sufficient condition for the ring of quotients with respect to a prime kernel functor to be semi-simple Artinian is found. &n analogous result for guasi-prime kernel functors is obtained in Section 5.
In Chapter II, the idea of controlling subgroups is applied to group ring localization. Some sufficient conditions for the descent of the maximal ring of quotients and of the classical ring of quotients are obtained in Section 8.
In Chapter III, characterizations of group rings, over nilpotent groups of transfinitely bounded cardinality, whose left global dimension is finite are obtained. As an application, this homological result is used to get information on the torsion elements of an M-group.
N2 - Three topics in localization theory and group ring theory are investigated.
In Chapter I, it is proved that every symmetric kernel functor in a left Noetherian ring is induced by a prime ideal. A sufficient condition for the ring of quotients with respect to a prime kernel functor to be semi-simple Artinian is found. &n analogous result for guasi-prime kernel functors is obtained in Section 5.
In Chapter II, the idea of controlling subgroups is applied to group ring localization. Some sufficient conditions for the descent of the maximal ring of quotients and of the classical ring of quotients are obtained in Section 8.
In Chapter III, characterizations of group rings, over nilpotent groups of transfinitely bounded cardinality, whose left global dimension is finite are obtained. As an application, this homological result is used to get information on the torsion elements of an M-group.
UR - https://open.library.ubc.ca/collections/831/items/1.0080276
ER - End of Reference