5 papers
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.
The Central Nullstellensatz over Centrally Algebraically Closed Division Rings
Masood Aryapoor
We introduce the concept of centrally algebraically closed division rings and show that a division ring satisfies the central Nullstellensatz if and only if it is centrally algebra…
A new notion of semiprime submodules
Masood Aryapoor
We introduce a new concept of a semiprime submodule. We show that a submodule of a finitely generated module over a commutative ring is semiprime if and only if it is radical, that…