A divisibility test of Arend Heyting, for polynomials over a …eld in an intuitionistic setting, may be thought of as a kind of division algorithm. We show that such a division algorithm holds for divisibility by polynomials of content 1 over any commutative ring in which nilpotent elements are zero. In addition, for an arbitary commutative ring R, we characterize those polynomials g such that t...

This paper is concerned with the factorization approach to control systems. The factorization approach we use here assumes that the plant admits coprime factorizations. On the ohter hand, the set of stable causal transfer functions is a general commutative ring. The objective of this paper is to present that even in the case where the set of stable causal transfer functions is a general commuta...

The Brauer group of a commutative ring is an important invariant of a commutative ring, a common journeyman to the group of units and the Picard group. Burnside rings of finite groups play an important rôle in representation theory, and their groups of units and Picard groups have been studied extensively. In this short note, we completely determine the Brauer groups of Burnside rings: they van...