On retracts and retractions of free modules over graded rings. (Q941266)

Let \(R=R_0\oplus R_1\oplus\cdots\) be a graded associative ring with a unit element. Suppose that \(f=f_0+f_{k_1}+\cdots+f_{k_n}\) is an idempotent matrix. The author finds some sufficient conditions under which \(f\) is conjugate to an idempotent matrix with entries from \(k_0\). For example it is the case if \(k_j\neq k_i+k_s\) for all \(j,i,s\). The problem of conjugation of idempotent matrices is equivalent to the statement that a projective finitely generated \(R\)-module \(P\) which is retract of a free \(R\)-module with a projection determined by \(f\) has the form \(P\simeq R\otimes_{R_0}Q\) for some projective \(R_0\)-module \(Q\).