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Z .JOURNAL OF ALGEBRA 179, 599 606 1996 ARTICLE NO. 0026

Summary: Z .JOURNAL OF ALGEBRA 179, 599 606 1996
Induction from Elementary Abelian Subgroups
E. Aljadeff* and Y. Ginosar
Department of Mathematics, Technion-Israel Institute of Technology, 32000 Haifa, Israel
Communicated by Kent R. Fuller
Received October 1, 1994
Let R be a ring with identity element 1 and G a finite group. RG
w xdenotes the group ring. Chouinard C showed that an RG-module M is
Z . Z .weakly projective projective iff it is RH weakly projective projective for
Zevery elementary abelian subgroup H of G see the definition of weak
.projective in Section 1 . His proof is based on Serre's theorem on products
Zof Bockstein operators. Chouinard's theorem can be generalized using his
.original result to arbitrary crossed products R)G. Recall that a crossed
product R)G is an associative ring which contains R and has an R basis
4u . The multiplicative structure is given by the rules:g G
Z . Z . Z . Z . Z1 ``Twisting'' u u s , u , where : G = G U R units
.of R .
Z . Z . Z . Z .2 ``Action'' u x s t x u where t g Aut R .


Source: Aljadeff, Eli - Department of Mathematics, Technion, Israel Institute of Technology


Collections: Mathematics