On weak annihilators and nilpotent associated primes of skew PBW extensions

Abstract

We investigate the notions of weak annihilator and nilpotent associated prime defined by Ouyang and Birkenmeier (Weak annihilator over extension rings, 2012) in the setting of skew PBW extensions. 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, noncommutative algebraic geometry, and theoretical physics. Finally, we present some ideas for future research.

Keywords:

• Nilpotent associated prime
• nilpotent good polynomial
• skew PBW extension
• weak annihilator

2020 Mathematics Subject Classification:

• 16D25
• 16N40
• 16S30
• 16S32
• 16S36
• 16S38

Additional information

Funding

This work was supported by Faculty of Science, Universidad Nacional de Colombia - Sede Bogotá, Colombia [Grant No. 52464].