On Generalized Periodic-Like Rings

On Generalized Periodic-Like Rings

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 some basic properties of such rings and prove some results on com...

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Main Authors: Howard E. Bell, Adil Yaqub
Format: Article
Language:English
Published: Hindawi Limited 2007-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2007/29513
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spelling doaj-cf1417d9536c4d11afc0d766109e40742020-11-24T21:32:40ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/2951329513On Generalized Periodic-Like RingsHoward E. Bell0Adil Yaqub1Department of Mathematics, Brock University, St. Catharines, Ontario L2S 3A1, CanadaDepartment of Mathematics, University of California, Santa Barbara, CA 93106, USALet 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 some basic properties of such rings and prove some results on commutativity.http://dx.doi.org/10.1155/2007/29513
collection DOAJ
language English
format Article
sources DOAJ
author Howard E. Bell
Adil Yaqub
spellingShingle Howard E. Bell
Adil Yaqub
On Generalized Periodic-Like Rings
International Journal of Mathematics and Mathematical Sciences
author_facet Howard E. Bell
Adil Yaqub
author_sort Howard E. Bell
title On Generalized Periodic-Like Rings
title_short On Generalized Periodic-Like Rings
title_full On Generalized Periodic-Like Rings
title_fullStr On Generalized Periodic-Like Rings
title_full_unstemmed On Generalized Periodic-Like Rings
title_sort on generalized periodic-like rings
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2007-01-01
description 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 some basic properties of such rings and prove some results on commutativity.
url http://dx.doi.org/10.1155/2007/29513
work_keys_str_mv AT howardebell ongeneralizedperiodiclikerings
AT adilyaqub ongeneralizedperiodiclikerings
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