منابع مشابه
On torsion-free periodic rings
There is a great deal of literature on periodic rings, respectively, torsion-free rings (especially of rank two). The aim of this paper is to provide a link between these two topics. All groups considered here are Abelian, with addition as the group operation. By order of an element we always mean the additive order of this element. All rings are associative but not necessarily with identity. T...
متن کاملOn Commutativity of Semiperiodic Rings
Let R be a ring with center Z, Jacobson radical J , and set N of all nilpotent elements. Call R semiperiodic if for each x ∈ R\ (J ∪Z), there exist positive integers m, n of opposite parity such that x − x ∈ N . We investigate commutativity of semiperiodic rings, and we provide noncommutative examples. Mathematics Subject Classification (2000). 16U80.
متن کاملRemarks on the Commutativity of Rings
Introduction. A celebrated theorem of N. Jacobson [7] asserts that if (1) x*(x) =x for every x in a ring R, where n(x) is an integer greater than one, then R is commutative. In a recent paper [2], I. N. Herstein has shown that it is enough to require that (1) holds for those x in R which are commutators: x= [y, z]=yz — zy of two elements of R. The purpose of this note is to show that if R has n...
متن کاملOn Jordan Isomorphisms of 2-torsion Free Prime Gamma Rings
This paper defines an isomorphism, an anti-isomorphism and a Jordan isomorphism in a gamma ring and develops some important results relating to these concepts. Using these results we prove Herstein’s theorem of classical rings in case of prime gamma rings by showing that every Jordan isomorphism of a 2-torsion free prime gamma ring is either an isomorphism or an anti-isomorphism. AMS Mathematic...
متن کاملA COMMUTATIVITY CONDITION FOR RINGS
In this paper, we use the structure theory to prove an analog to a well-known theorem of Herstein as follows: Let R be a ring with center C such that for all x,y ? R either [x,y]= 0 or x-x [x,y]? C for some non negative integer n= n(x,y) dependingon x and y. Then R is commutative.
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1984
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700001969