New instances of equivariant Noetherianity

Abstract: When a group or monoid G acts on a ring R by means of endomorphisms, we say that R is G-Noetherian if every ascending chain of G-stable ideals in R is eventually constant; and we call R *topologically* G-Noetherian if this condition holds at least for chains of G-stable radical ideals.

Over the last 15 years, many examples of (topologically) G-Noetherian rings have been discovered. I will first discuss some of the older results and their motivation. Here G is usually the infinite symmetric group Sym or the infinite general linear group GL over an infinite field.

After that, I will turn to recent joint work with Chiu-Danelon-Eggermont-Farooq on examples where G=Sym x GL; and with Blatter-Rupniewski on examples where G=GL over a finite field.

commutative algebra

Audience: researchers in the topic

Fellowship of the Ring

Series comments: Description: National Commutative Algebra Seminar

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