Theoretical analysis demonstrates radical classifications in Ore extensions, highlighting structural connections between base rings and differential polynomial systems.
Let [Formula: see text] be a ring, [Formula: see text] be an automorphism of [Formula: see text] and [Formula: see text] be a [Formula: see text]-derivation of [Formula: see text]. We use [Formula: see text] to denote the set of all words composed of [Formula: see text], [Formula: see text] and [Formula: see text]. A [Formula: see text]-ideal [Formula: see text] of [Formula: see text] is [Formula: see text]-prime if whenever [Formula: see text] are such that [Formula: see text] for any [Formula: see text], we have [Formula: see text] or [Formula: see text]. In this paper, we first introduce the [Formula: see text]-prime ideal and the [Formula: see text]-prime radical of a ring [Formula: see text], to obtain connections between the prime radical of the Ore extension [Formula: see text] and the [Formula: see text]-prime radical of the base ring [Formula: see text]. Based on these results, we next give definitions of the [Formula: see text]-LS-prime ideal, the [Formula: see text]-strongly prime ideal and the [Formula: see text]-uniformly strongly prime ideal of a ring [Formula: see text] to provide formulas for the LS-prime radical, the strongly prime radical and the uniformly strongly prime radical of the Ore extension.
No takes yet. Share an insight, caveat, or question.
Kim et al. (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: