Power automorphisms of finite p-groups

Abstract

In this paper, the definitions of quasi-orthogonal idempotent sequences and Iq-dimensions of a ring R are given. The relations between Iq-dimensions and block decomposition numbers of a ring are discussed. As a generalization of monic polynomials, the concept of quasi-monic polynomials over a ring is introduced. It is shown that, for a quasi-monic polynomial over a ring, the division algorithm holds. Suslin Lemma and Horrocks' Theorem are extended to the setting of quasi-monic polynomials. For a commutative ring R, if f(x) is a quasi-monic polynomial in R[x], then GD(R) = GD(R[x]/f(x)) is proved, where GD(R) denotes the global dimension of R.