On a commutativity theorem for semi-simple rings
نویسندگان
چکیده
منابع مشابه
A Commutativity Theorem for Associative Rings
Let m > 1; s 1 be xed positive integers, and let R be a ring with unity 1 in which for every x in R there exist integers p = p(x) 0; q = q(x) 0;n = n(x) 0; r = r(x) 0 such that either x p x n ; y]x q = x r x; y m ]y s or x p x n ;y]x q = y s x; y m ]x r for all y 2 R. In the present paper it is shown that R is commutative if it satisses the property Q(m) (i.e. for all x; y 2 R;mx; y] = 0 implie...
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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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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.
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1985
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700009321