The number of idempotents in abelian group rings

Peter Danchev
2012 Filomat  
Suppose that R is a commutative unitary ring of arbitrary characteristic and G is a multiplicative abelian group. Our main theorem completely determines the cardinality of the set id(RG), consisting of all idempotent elements in the group ring RG. It is explicitly calculated only in terms associated with R, G and their divisions. This result strengthens previous estimates obtained in the literature recently.
doi:10.2298/fil1204719d fatcat:rlbsgjwzn5e67jlrv7vnmh56a4