Abstract
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).
Highlights
The last is just equivalent to the desired equality
We will further identify with no loss of generality ( i∈I Ri)A with i∈I (RiA), and (×j∈J Kj)G with ×j∈J (KjG), so that the two isomorphisms in points (a) and (b) will be formal equalities
Suppose R is a perfect ring with a finite number of idempotents
Summary
Let A be a finite group and let K = ×j∈J Kj be a finite direct product of rings. We will further identify with no loss of generality ( i∈I Ri)A with i∈I (RiA), and (×j∈J Kj)G with ×j∈J (KjG), so that the two isomorphisms in points (a) and (b) will be formal equalities, . Suppose G is a group whose factor G0/Gp is finite and R = i∈I Ri where each Ri is indecomposable for i ∈ I.
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