On rings with “solvability” conditions
نویسندگان
چکیده
منابع مشابه
Subperiodic Rings with Conditions on Extended Commutators
Let R be a ring with Jacobson radical J and with center C. Let P be the set of potent elements x for which xk = x for some integer k > 1. Let N be the set of nilpotents. A ring R is called subperiodic if R \ (J ∪ C) ⊆ N + P . We consider the commutativity behavior of a subperiodic ring with some constraint involving extended commutators. Mathematics Subject Classification: 16U80, 16D70
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Throughout this paper, R is an associative ring; andN ,C,C(R), and J denote, respectively, the set of nilpotent elements, the center, the commutator ideal, and the Jacobson radical. An element x of R is called potent if xn = x for some positive integer n= n(x) > 1. A ring R is called periodic if for every x in R, xm = xn for some distinct positive integersm=m(x), n = n(x). A ring R is called we...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1974
ISSN: 0021-8693
DOI: 10.1016/0021-8693(74)90136-7