Geodesic
On a Theorem of Herstein
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1348-1353

Voir la notice de l'article provenant de la source Cambridge University Press

Throughout this paper, Z is the ring of integers, ƒ*(t) (ƒ(t)) is an integer monic (co-monic) polynomial in the indeterminate t (i.e., each coefficient of ƒ* (ƒ) is in Z and its highest (lowest) coefficient is 1 (5, p. 121, Definition) and M* (M) is the multiplicative semigroup of all integer monic (co-monic) polynomials ƒ* (ƒ) having no constant term. In (3, Theorem 2), Herstein proved that if R is a division ring with centre C such that 1 then R = C. In this paper we seek a generalization of Herstein's result to semi-simple rings. We also study the following condition: (1)* Our results are quite complete for a semi-simple ring R in which there exists a bound for the codegree ofƒ (ƒ*) (i.e., the degree of the lowest monomial of ƒ(ƒ*)) appearing in the left-hand side of (1) ((1)*). 
Chacron, M. On a Theorem of Herstein. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1348-1353. doi: 10.4153/CJM-1969-148-5
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