# Ring detail

## Name: Kolchin's simple V-domain

Description: Let $k$ be a universal differential field with derivation $D$, and let $R=k[y, D]$ be the differential polynomial ring. (Underlying set and addition operation is the same as $k[y]$, and $ya=ay+D(a)$.)

Notes: Has a unique simple right $R$ module (up to isomorphism)

Keywords differential polynomial ring

Reference(s):

• J. H. Cozzens. Homological properties of the ring of differential polynomials. (1970) @ Section 1

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