Since the foundation paper of M. Auslander and 0. Goldman [ 1 J, several authors have generalized constructions for studying group algebras over fields to separable algebras over commutative rings. Specifically, we have in mind the Schur index [20], the Schur exponent [18], the Schur group [S], and the uniform group [ 111. This paper gives additional properties of these constructions and studie...

It is said to be Hurwitz stable if the real part of all zeros of the polynomial (1) are negative; It is said to be Schur stable if all zeros of the polynomial (1) lie within unit circle. By matrix theory, Gantmacher (1964), algebraic criteria on Hurwitz stability for continuous linear systems can be directly derived from calculation of a Cauchy index of a rational fraction ) (x R , namely ) (x ...

In this paper, the performance of SVD and Schur decomposition is evaluated and compared for image copyright protection applications. The watermark image is embedded in the cover image by using Quantization Index Modulus Modulation (QIMM) and Quantization Index Modulation (QIM). Watermark image is embedded in the D matrix of Schur decomposition and Singular Value Decomposition (SVD). Watermarkin...

We give examples of finite string C -groups (the automorphism groups abstract regular polytopes) that have irreducible characters real Schur index 2. This answers a problem Monson concerning these groups.

The Schur group of a commutative ring, R, with identity consists of all classes in the Brauer group of R which contain a homomorphlc image of a group ring RG for some finite group G. It is the purpose of ths article to continue an investigation of this group which was introduced in earler work as a natural gene=allzatlon of the Schur group of a field. We generalize certain facts pertaining to t...