A Note on Elementary Derivations

2000 Mathematics Subject Classification: Primary: 14R10. Secondary: 14R20, 13N15.

On the Range and the Kernel of Derivations

2000 Mathematics Subject Classification: Primary 47B47, 47B10; Secondary 47A30.

A Note About the Nowicki Conjecture on Weitzenböck Derivations

2000 Mathematics Subject Classification: 13N15, 13A50, 16W25.

Weitzenböck Derivations and Classical Invariant Theory: I. Poincaré Series

2000 Mathematics Subject Classification: 13N15, 13A50, 16W25.

Weitzenböck Derivations and Classical Invariant Theory II: The Symbolic Method

2000 Mathematics Subject Classification: 13N15, 13A50, 13F20.

Generalized Derivations and Norm Equality in Normed Ideals

2000 Mathematics Subject Classification: 47A10, 47A12, 47A30, 47B10, 47B20, 47B37, 47B47, 47D50.

A Survey of Counterexamples to Hilbert's Fourteenth Problem

We survey counterexamples to Hilbert’s Fourteenth Problem, beginning with those of Nagata in the late 1950s, and including recent counterexamples in low dimension constructed with locally nilpotent derivations. Historical framework and pertinent references are provided. We also include 8 important open questions.