Lei Qiao, Qianyu Shu, Fanggui Wang. Source: Journal of Commutative Algebra, Volume 12, Number 3, 435--445.Abstract:
In this paper, we characterize Prüfer [math] -multiplication domains as integral domains which have the property that the existence of a generalized solution of any system of linear equations is equivalent to a weak equality of the determinantal ideals of the coefficient matrix and the augmented matrix of the system. In fact, we obtain a more general result for commutative rings of weak global [math] -dimension (in the sense of Bueso, Van Ostaeyen and Verschoren) at most one, where [math] is a half-centered hereditary torsion theory.