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On the Specht property of some varieties of associative rings. (Russian) Zbl 0534.16015
Let \(F={\mathbb{Z}}<X_ 1,X_ 2,...>\) be the free associative ring on a countable free generating set \(X_ 1,X_ 2,...\). A fully characteristic (T-ideal) Q of F is called Spechtian if it is finitely generated as a T- ideal and if the T-ideals containing Q satisfy the ascending chain condition. The reviewer and M. V. Volkov have shown that a T-ideal, which is generated by the polynomial \(X^ 2-X^ n\) (\(n\neq 2)\), is Spechtian [Algebra Logika 20, 155-164 (1981; Zbl 0497.16006)]. The authors give a short new proof of this result.
Reviewer: Yu.N.Mal’tsev
MSC:
16Rxx Rings with polynomial identity
16Dxx Modules, bimodules and ideals in associative algebras
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