Ring $R_{ 108 }$

Kolchin's simple V-domain


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


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

  • = has the property
  • = does not have the property
  • = information not in database
Name Measure
global dimension left: 1right: 1
Name Description
Idempotents $\{0,1\}$
Jacobson radical $\{0\}$
Left singular ideal $\{0\}$
Left socle $\{0\}$
Nilpotents $\{0\}$
Right singular ideal $\{0\}$
Right socle $\{0\}$
Zero divisors $\{0\}$