2022/03/18 by Sebastián Higuera, Higuera, Sebastián, Armando Reyes +1 · 1 citation
Mathematics · #16D25 #16N40 #16S30 #16S32 #16S36 #16S38 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2203.09912
openalex publication_date 2022/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the notions of weak annihilator and nilpotent associated prime defined by Ouyang and Birkenmeier \citeOuyangBirkenmeier2012 in the setting of noncommutative rings having PBW bases. We extend several results formulated in the literature concerning annihilators and associated primes of commutative rings and skew polynomial rings to a more general setting of algebras not considered before. We exemplify our results with families of algebras appearing in the theory of enveloping algebras, differential operators on noncommutative spaces, noncommutative algebraic geometry, and theoretical physics. Finally, we present some ideas for future research.