Principal systems of ideals (Q1085211)

A principal system K of ideals of a Noetherian ring R is such that if b is nonmaximal in K then, for some x in R, (b,x)\(\in K\) and either \((1)\quad b:x=b\) and \(\cap_{n\geq 1}(b,x^ n)=b,\quad or\) \((2)\quad c\supset b,\) \(c:x=c\) and xc\(\subseteq b\) for some c in K. This extends a notion of \textit{M. Hochster} and \textit{J. A. Eagon} [Am. J. Math. 93, 1020- 1058 (1971; Zbl 0244.13012)]. The author's main applications concern R- sequences. Conditions are given for principal systems to extend under a ring homomorphism.