Generalized Clifford Theory (Group Ring, Frobenius Extensions)

Let R and S be two rings with identity elements and let l : R (--->) S be a ring homomorphism preserving their identity elements. Then any S-module W can be regarded as an R-module W(,R). Also, for any right R-module V, we can form the "induced" S-Module V('S) = V (CRTIMES)(,R) S. Fixing a right R-module V, we let A = End(,R)(V) and B = End(,S)(V('S)). Then there is a natural ring homomorphism l' : A (--->) B. The R-module V is said to be weakly S-invariant if V('S) is isomorphic to a direct summand of a direct sum of a finite number of copies of V as R-modules. (We say that (V('S))(,R) weakly divides V in this case.)

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Uno, Katsuhiro

• Mathematics

Identifier

(UMI)AAI8511681

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/71232