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A note on linear derivations

Amit Patra — 2024

Czechoslovak Mathematical Journal

At first we prove some results on a general polynomial derivation using few results of linear derivation. Then we study the ring of constants of a linear derivation for some rings. We know that any linear derivation is a nonsimple derivation. In the last section we find the smallest integer $w > 1$ such that the polynomial ring in $n$ variables is $w$ -differentially simple, all $w$ derivations are nonsimple and the $w$ derivations set contains a linear derivation.

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