Generalized periodic and generalized Boolean rings
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 imply the commutativity of a generalized periodic,...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201005713 |
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| _version_ | 1832553453396688896 |
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| author | Howard E. Bell Adil Yaqub |
| author_facet | Howard E. Bell Adil Yaqub |
| author_sort | Howard E. Bell |
| collection | DOAJ |
| description | 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 imply the commutativity of a generalized periodic, or a generalized Boolean, ring. |
| format | Article |
| id | doaj-art-355407dec91a45b78e0454bc3c389666 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-355407dec91a45b78e0454bc3c3896662025-02-03T05:53:57ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0126845746510.1155/S0161171201005713Generalized periodic and generalized Boolean ringsHoward E. Bell0Adil Yaqub1Department of Mathematics, Brock University, Ontario, Street Catharines L2S 3A1, CanadaDepartment of Mathematics, University of California, Santa Barbara, CA 93106, USAWe 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 imply the commutativity of a generalized periodic, or a generalized Boolean, ring.http://dx.doi.org/10.1155/S0161171201005713 |
| spellingShingle | Howard E. Bell Adil Yaqub Generalized periodic and generalized Boolean rings International Journal of Mathematics and Mathematical Sciences |
| title | Generalized periodic and generalized Boolean rings |
| title_full | Generalized periodic and generalized Boolean rings |
| title_fullStr | Generalized periodic and generalized Boolean rings |
| title_full_unstemmed | Generalized periodic and generalized Boolean rings |
| title_short | Generalized periodic and generalized Boolean rings |
| title_sort | generalized periodic and generalized boolean rings |
| url | http://dx.doi.org/10.1155/S0161171201005713 |
| work_keys_str_mv | AT howardebell generalizedperiodicandgeneralizedbooleanrings AT adilyaqub generalizedperiodicandgeneralizedbooleanrings |