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The Gleason problem for $$\mathbb A^k(\Omega)$$, $$\mathbb H^k(\Omega)$$, $$\text{Lip}_{k=\varepsilon} (\Omega)$$. (English) Zbl 1037.32008
Let $$\Omega$$ be a domain in $$\mathbb C^n$$ and $$\mathbb A(\Omega)$$ be the algebra of functions holomorphic in $$\Omega$$ and continuous on the closure of $$\Omega$$.
The author compares the maximal ideal $$m_p$$ in $$\mathbb A(\Omega)$$ given by all the functions vanishing at a point $$p\in \Omega$$ to the ideal generated by $$z_1-p_1,\dots, z_n- p_n$$.
##### MSC:
 32A38 Algebras of holomorphic functions of several complex variables 32B05 Analytic algebras and generalizations, preparation theorems 46E25 Rings and algebras of continuous, differentiable or analytic functions
##### Keywords:
algebra of holomorphic functions; maximal ideals
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