Author: Adil Yaqub 1
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  • 1 Department of Mathematics, University of California Santa Barbara, CA 93106, U.S.A.
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A ring R is called periodic if, for every x in R, there exist distinct positive integers m and n such that xm=xn. An element x is called potent if xk=x for some integer k≯1. A ring R is called weakly periodic if every x in R can bewritten in the form x=a+b for some nilpotent element a and some potent element b. A ring R is called weakly periodic-like if every x in R which is not in the center of R can be written in the form x=a+b, where a is nilpotent and b is potent. Our objective is to study the structure of weakly periodic-like rings, with particular emphasis on conditions which yield such rings commutative, or conditions which render the nilpotents N as an ideal of R and R/N as commutative.

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