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FI -modules over Noetherian rings

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In this paper we study representation theory of the category FI$^m$ introduced by Gadish which is a product of copies of the category FI, and show that quite a few… Click to show full abstract

In this paper we study representation theory of the category FI$^m$ introduced by Gadish which is a product of copies of the category FI, and show that quite a few interesting representational and homological properties of FI can be generalized to FI$^m$ in a natural way. In particular, we prove the representation stability property of finitely generated FI$^m$-modules over fields of characteristic 0.

Keywords: noetherian rings; modules noetherian

Journal Title: Journal of Pure and Applied Algebra
Year Published: 2019

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