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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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