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Tjurina Ideal

The Tjurina ideal of a formal power series f in R=k[[x_1,...,x_n]] is the ideal generated by f and all its partial derivatives:

I_f=(f,partialf/partialx_1,...,partialf/partialx_n)=(J_f,f),

where J_f is the Jacobian ideal. If f(0)=0 and f has an isolated critical point at the origin, the finite dimension dim_k(R/I_f) is the Tjurina number (Zhang and Zuo 2026).

See also

Euler Conductor, Jacobian Ideal, Quotient Ring

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References

Zhang, Y. and Zuo, H. "The Hassanzadeh-Nasrollah Nejad-Simis Conjecture on Euler Conductors." 7 Oct 2026. https://arxiv.org/abs/2610.09833.

Cite this as:

Weisstein, Eric W. "Tjurina Ideal." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TjurinaIdeal.html

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