Hazar Abu-Khuzam
University of California, Santa Barbara
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Featured researches published by Hazar Abu-Khuzam.
International Journal of Mathematics and Mathematical Sciences | 1981
Hazar Abu-Khuzam; Adil Yaqub
Let n be a fixed positive integer. Let R be a ring with identity which satisfies (i) xnyn=ynxn for all x,y in R, and (ii) for x,y in R, there exists a positive integer k=k(x,y) depending on x and y such that xkyk=ykxkand (n,k)=1. Then R is commutative. This result also holds for a group G. It is further shown that R and G need not be commutative if any of the above conditions is dropped.
International Journal of Mathematics and Mathematical Sciences | 2006
Hazar Abu-Khuzam; Adil Yaqub
Let R be a ring such that every zero divisor x is expressible as a sum of a nilpotent element and a potent element of R:x=a
International Journal of Mathematics and Mathematical Sciences | 2005
Hazar Abu-Khuzam; Howard E. Bell; Adil Yaqub
A ring is called semi-weakly periodic if each element which is not in the center or the Jacobson radical can be written as the sum of a potent element and a nilpotent element. After discussing some basic properties of such rings, we investigate their commutativity behavior.
International Journal of Mathematics and Mathematical Sciences | 1994
Hazar Abu-Khuzam; Adil Yaqub
Let R be a ring, and let C denote the center of R. R is said to have a prime center if whenever ab belongs to C then a belongs to C or b belongs to C. The structure of certain classes of these rings is studied, along with the relation of the notion of prime centers to commutativity. An example of a non-commutative ring with a prime center is given.
International Journal of Mathematics and Mathematical Sciences | 1988
Hazar Abu-Khuzam
We give the structure of certain rings which are multiplicatively generated by nilpotents or multiplicatively generated by idempotents and nilpotents.
International Journal of Mathematics and Mathematical Sciences | 1984
Hazar Abu-Khuzam; Adil Yaqub
Let R be a ring (not necessarily with identity) and let N denote the set of nilpotent elements of R. Suppose that (i) N is commutative, (ii) for every x in R, there exists a positive integer k=k(x) and a polynomial f(λ)=fx(λ) with integer coefficients such that xk=xk
International Journal of Mathematics and Mathematical Sciences | 1983
Hazar Abu-Khuzam; Adil Yaqub
Let R be a ring and let N denote the set of nilpotent elements of R. Let Z denote the center of R. Suppose that (i) N is commutative, (ii) for every x in R there exists x′ϵ such that x−x2x′ϵN, where denotes the subring generated by x, (iii) for every x,y in R, there exists an integer n=n(x,y)≥1 such that both (xy)n−(yx)n and (xy)n
Bulletin of The Australian Mathematical Society | 1983
Hazar Abu-Khuzam
Bulletin of The Australian Mathematical Society | 1980
Hazar Abu-Khuzam; Adil Yaqub
Mathematical journal of Okayama University | 1980
Hazar Abu-Khuzam; Hisao Tominaga; Adil Yaqub