Simple modules over skew polynomial rings
 
 
Description: 

We consider the structure of modules over Noetherian rings. A Noetherian ring S whose simple modules have the property that their finitely generated essential extensions are Artinian is said to satisfy property (⋄). For commutative Noetherian rings the validity of (⋄) is due to Matlis (1958).
In this talk we will discuss (⋄) for skew polynomial rings S = R[θ; α] where R is a commutative Noetherian ring and α is an automorphism of R, with the indeterminate θ satisfying the relation θr = α(r)θ for all r ∈ R.
A complete characterization is found when R is an affine algebra over a field K and α is a K-automorphism. We will discuss in some detail the case when R = C[x, y] and α is a C-algebra automorphism and indicate some open questions.

 

This talk is based on a paper with Ken Brown and Jerzy Matczuk.

Date:  2022-01-13
Start Time:   11:30
Speaker:  Paula Carvalho (CMUP, FCUP)
Institution:  CMUP, FCUP
Place:  Room 004, UP Math. Dept.
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