Generalized J-Rings and Commutativity
نویسندگان
چکیده
A J-ring is a ring R with the property that for every x in R there exists an integer n(x)>1 such that x x x n = ) ( , and a well-known theorem of Jacobson states that a Jring is necessarily commutative. With this as motivation, we define a generalized Jring to be a ring R with the property that for all x, y in R0 there exists integers 1 ) ( , 1 ) ( > = > = y m m x n n such that m n xy y x − is nilpotent, where R0 is a certain subset of R. The commutativity behavior of such rings is considered. Mathematics Subject Classification: 16U80, 16D70
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