Associated prime ideals over skew PBW extensions

Abstract

In this article, we continue the study of ideals of the noncommutative rings of polynomial type known as skew Poincaré-Birkhoff-Witt extensions. More exactly, we focus on the associated prime ideals of these extensions. Our purpose here is to describe how the associated primes of a ring of coefficients behave under passage to a skew PBW extension over this ring. As we show, all results established here coincide and generalize those corresponding in the commutative case and the Ore extensions.

Keywords:

• Associated prime ideal
• noncommutative ring
• skew PBW extension

2010 Mathematics Subject Classification:

• 16D25
• 16N40
• 16P40
• 16S30
• 16S36
• 16S38

Acknowledgements

The third named author was supported by the research fund of Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia, HERMES CODE 41535.