HOMOGENEOUS IDEALS AND JACOBSON RADICAL

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Submitted: 2025-02-06; Published: 2025-02-06

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Abstract

In this paper the Jacobson radical of an algebraF⟨X⟩/H is studied, where FhXi is a free associative algebra of countable rank over infinite field F and H is a homogeneous ideal of the algebrF⟨X⟩. The following theorem is proved: the Jacobson radical of an algebra F⟨X⟩/H is a nil ideal.