On stable orthogonal decompositions of idempotents
The paper is concerned with Green's indecomposability theorem which asserts that the induced module of an absolutely indecomposable module from a subnormal subgroup of \(p\)-primary index is absolutely indecomposable. The authors are using here \textit{L. Puig}'s approach [Math. Z. 166, 117-129 (1979; Zbl 0395.16006)] to prove a generalization of Green's theorem to the case of an arbitrary complete discrete valuation ring \(\mathcal O\) with residue field \(k\) of characteristic \(p\). They prove general results characterizing the freeness relative to a subnormal subgroup of a relative projective pointed group on a \(G\)-algebra. If the subnormal subgroup has \(p\)-primary index, then the condition is satisfied if \(p\) does not divide the degree of a certain separable extension of \(k\).
scientific article; zbMATH DE number 1340569