Demotions of ideals in commutative rings with applications to normally torsion-freeness
Abstract
Let J ⊂eq I be ideals in a commutative Noetherian ring R, and r,s ≥ 0. We say that J is a demotion of I if Ir Js = Ir+s Js for all r,s ≥ 0. In this paper, we mainly aim to explore this notion in polynomial rings. In particular, we investigate the relation between the demotion property and normal torsion-freeness. Furthermore, we compare the reductions of ideals and demotions of ideals.
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