A CONDITION GUARANTEEING COMMUTATIVITY
نویسندگان
چکیده
منابع مشابه
A condition Guaranteeing Commutativity
We give a simple characterization for a nonassociative algebra A, having characteristic 6= 2, to be commutative. Namely, A is commutative if and only if it is exible with a commuting set of generators. A counterexample shows that characteristic 6= 2 is necessary. Both the characterization and the counterexample were discovered using the computer algebra system in [2].
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In view of this result, it was conjectured that any ring with only finitely many noncentral subrings is either finite or commutative. It is our principal goal to prove this conjecture; and in the process we provide a new proof of Theorem 1.1. For any ring R, the symbols N, D, Z , and ℘(R) will denote, respectively, the set of nilpotent elements, the set of zero divisors, the center, and the pri...
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: International Journal of Algebra and Computation
سال: 1992
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196792000177