** Riv.Mat.Univ.Parma (6) 4 (2001) **

**MICHAEL G. VOSKOGLOU**

*Differential simplicity and dimension of a commutative ring*

**Pages:** 111-119

**Received:** 5 February 2001

**Mathematics Subject Classification (2000):** 13N15

**Abstract**:

In the present paper the differential simplicity of a commutative ring is studied with respect to its dimension.
It is shown that a d-simple ring of prime characteristic is 0-dimensional.
In the case of characteristic zero a necessary and sufficient condition is given for the d-simplicity of a
1-dimensional finitely generated algebra over a field k and examples are presented of rings with dimension greater
than 1 and even of infinite dimension (polynomial rings).

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