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 AA be an ll-generated semiring with commutative addition in which the identity xm=0xm=0 is satisfied. Then the nilpotency index of AA is not greater than 2lm+1m32lm+1m3. Nagata–Higman theorem for general semirings. If an ll-generated semiring satisfies the identity xm=0xm=0 than every word in it of length greater than mm⋅2lm+1m3+mmm⋅2lm+1m3+m is zero.
|Original language||American English|
|Journal||Fundamentalnaya i Prikladnaya Matematika (Moscow)|
|State||Published - 1995|
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