FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1995, VOLUME 1, NUMBER 2, PAGES 523-527

The Nagata-Higman theorem for semirings

A.Ya.Belov

This paper contains the proof of the Nagata-Higman theorem for semirings (with non-commutative addition in general). The main results are the following:

Theorem. Let A be an l-generated semiring with commutative addition in which the identity x^m = 0 is satisfied. Then the nilpotency index of A is not greater than 2 l^m+1 m³.

Nagata-Higman theorem for general semirings. If an l-generated semiring satisfies the identity x^m = 0 than every word in it of length greater than m^m 2 l^m+1 m³ + m$ is zero.

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Location: http://mech.math.msu.su/~fpm/eng/95/952/95212.htm
Last modified: October 7, 1997.