Geodesic
The Nagata–Higman theorem for hemirings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 3, pp. 651-658
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper the hemirings (in general, with noncommutative addition) with the identity $x^n=0$ are studied. The main results are the following ones. Theorem. If a $n!$-torsionfree general hemiring satisfies the identity $x^n=0$, then it is nilpotent. The estimates of the nilpotency index are equal for $n!$-torsionless rings and general hemirings. Theorem. The estimates of the nilpotency index of $l$-generated rings and general hemirings with identity $x^n=0$ are equal. The proof is based on the following lemma. Lemma. If a general semiring $S$ satisfies the identity $x^n=0$, then $S^n$ is a ring. 
@article{FPM_2001_7_3_a1,
     author = {I. I. Bogdanov},
     title = {The {Nagata{\textendash}Higman} theorem for hemirings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {651--658},
     year = {2001},
     volume = {7},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_3_a1/}
}
TY  - JOUR
AU  - I. I. Bogdanov
TI  - The Nagata–Higman theorem for hemirings
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2001
SP  - 651
EP  - 658
VL  - 7
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/FPM_2001_7_3_a1/
LA  - ru
ID  - FPM_2001_7_3_a1
ER  - 
%0 Journal Article
%A I. I. Bogdanov
%T The Nagata–Higman theorem for hemirings
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2001
%P 651-658
%V 7
%N 3
%U http://geodesic.mathdoc.fr/item/FPM_2001_7_3_a1/
%G ru
%F FPM_2001_7_3_a1
I. I. Bogdanov. The Nagata–Higman theorem for hemirings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 3, pp. 651-658. http://geodesic.mathdoc.fr/item/FPM_2001_7_3_a1/