We calculate Warfield p-invariants Wα,p(V (RG)) of the group of normalized units V (RG) in a commutative group ring RG of prime char(RG) = p in each of the following cases: (1) G0/Gp is finite and R is an arbitrary direct product of indecomposable rings; (2) G0/Gp is bounded and R is a finite direct product of fields; (3) id(R) is finite (in particular, R is finitely generated). Moreover, we give a general strategy for the computation of the above Warfield p-invariants under some restrictions on R and G. We also point out an essential incorrectness in a recent paper due to Mollov and Nachev in Commun. Algebra (2011).
@article{10822,
title = {Warfield p-Invariants in Abelian Group Rings of Characteristic p},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {31},
year = {2013},
doi = {10.5269/bspm.v31i2.10822},
language = {EN},
url = {http://dml.mathdoc.fr/item/10822}
}
Danchev, Peter. Warfield p-Invariants in Abelian Group Rings of Characteristic p. Boletim da Sociedade Paranaense de Matemática, Tome 31 (2013) . doi : 10.5269/bspm.v31i2.10822. http://gdmltest.u-ga.fr/item/10822/