5 citations · 17 across the 27 of their papers we have counts for
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Strong and Explicit Forms of the One-Sided Nullstellensatz over Division Rings
Masood Aryapoor
We establish strong and explicit forms of a one-sided Nullstellensatz for polynomial rings D[x1, . . . , xn] over arbitrary division rings D with central indeterminates. To this en…
Integral Dependence over One-Sided Ideals, Part I: Foundations and Classical Applications
Masood Aryapoor
We introduce notions of integrality and full integrality over one-sided ideals, together with associated radical constructions, and develop a general framework for their study. As…
Involutions in the Cayley-Dickson construction
Masood Aryapoor, Per Bäck, Sophie Pautrel
We determine all involutions in the Cayley-Dickson construction that extend the involution of the original -algebra. We also find all algebra isomorphisms between the resulting…
Hilbert's Basis Theorem for generalized nonassociative Ore extensions
Per Bäck, Masood Aryapoor
We introduce a broader class of nonassociative Ore extensions that unifies and generalizes several earlier constructions. We prove generalizations of Hilbert's Basis Theorem for th…
Amitsur--Small Extensions and a Skew Amitsur--Small Theorem
Masood Aryapoor
We introduce the notion of Amitsur--Small extensions to generalize a key lemma underlying the Amitsur--Small Theorem to the skew setting. Building on this framework, we establish a…
Prime One-Sided Ideals in Principal Ideal Domains
Masood Aryapoor
This article investigates various notions of primeness for one-sided ideals in noncommutative rings, with a focus on principal ideal domains.