Zobrazeno 1 - 10
of 90
pro vyhledávání: '"Adil Yaqub"'
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 2005, Iss 9, Pp 1387-1391 (2005)
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
Externí odkaz:
https://doaj.org/article/e26ea76c0e53487fa95a6fd7a805b09d
Autor:
Amber Rosin, Adil Yaqub
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 2003, Iss 33, Pp 2097-2107 (2003)
Our objective is to study the structure of subweakly periodic rings with a particular emphasis on conditions which imply that such rings are commutative or have a nil commutator ideal. Related results are also established for weakly periodic (as well
Externí odkaz:
https://doaj.org/article/ade4dae98429409596868b18684a661d
Autor:
Adil Yaqub
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 25, Iss 5, Pp 299-304 (2001)
A well-known theorem of Jacobson (1964, page 217) asserts that a ring R with the property that, for each x in R, there exists an integer n(x)>1 such that xn(x)=x is necessarily commutative. This theorem is generalized to the case of a weakly periodic
Externí odkaz:
https://doaj.org/article/ca3ea02c16c2427e9f1ea59817d99bad
Autor:
Howard E. Bell, Adil Yaqub
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 26, Iss 8, Pp 457-465 (2001)
We prove that a generalized periodic, as well as a generalized Boolean, ring is either commutative or periodic. We also prove that a generalized Boolean ring with central idempotents must be nil or commutative. We further consider conditions which im
Externí odkaz:
https://doaj.org/article/355407dec91a45b78e0454bc3c389666
Autor:
Howard E. Bell, Adil Yaqub
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 19, Iss 1, Pp 87-92 (1996)
Let R be a ring, and let N and C denote the set of nilpotents and the center of R, respectively. R is called generalized periodic if for every x∈R\(N⋃C), there exist distinct positive integers m, n of opposite parity such that xn−xm∈N⋂C. We
Externí odkaz:
https://doaj.org/article/ad1395bbfb8c4ade9767a5695c231e22
Autor:
Hazar Abu-Khuzam, Adil Yaqub
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 17, Iss 4, Pp 667-670 (1994)
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 o
Externí odkaz:
https://doaj.org/article/ed55dffc94ee4b9ea39b663135ea8684
Autor:
Howard E. Bell, Adil Yaqub
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 2007 (2007)
Let R be a ring with center Z, Jacobson radical J, and set N of all nilpotent elements. Call R generalized periodic-like if for all x∈R∖(N∪J∪Z) there exist positive integers m, n of opposite parity for which xm−xn∈N∩Z. We identify som
Externí odkaz:
https://doaj.org/article/cf1417d9536c4d11afc0d766109e4074
Autor:
Hazar Abu-Khuzam, Adil Yaqub
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 2006 (2006)
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+b, where a is nilpotent, b is potent, and ab=ba. We call such a ring a D*-ring. We give the structure of periodic D*-ring, wea
Externí odkaz:
https://doaj.org/article/93dbcd310b714fc9bbf38fa768ff31f0
Autor:
Mohan S. Putcha, Adil Yaqub
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 2, Iss 1, Pp 121-126 (1979)
Let R be a ring and let N denote the set of nilpotent elements of R. Let n be a nonnegative integer. The ring R is called a θn-ring if the number of elements in R which are not in N is at most n. The following theorem is proved: If R is a θn-ring,
Externí odkaz:
https://doaj.org/article/f7f74bfa8a5d4f9ea60a74e7e8332a83
Autor:
Hazar Abu-Khuzam, Adil Yaqub
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 4, Iss 1, Pp 101-107 (1981)
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 commutativ
Externí odkaz:
https://doaj.org/article/423d95122b22484a98c73ef9545cea2b