This article is cited in 1 paper

On nilpotency of graded associative algebras

A. D. Chanyshev

M. V. Lomonosov Moscow State University

Abstract: It is proved that an associative PI-algebra over a field of characteristic zero that is graded by an arbitrary semigroup and that satisfies the relation $a^n=0$ for all homogeneous elements and is generated by a finite number of its homogeneous components is nilpotent. This generalizes a well-known theorem of M. Nagata.

UDC: 512.554

MSC: Primary 16W50, 16R10; Secondary 16N40

Received: 18.07.1989

 English version: Mathematics of the USSR-Sbornik, 1992, 71:2, 419–425

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