Generalized periodic rings
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 prove that a generalized periodic ring always has the set N...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171296000130 |
| Summary: | 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 prove that a generalized periodic ring always has the set N of nilpotents forming an ideal in R. We also consider some conditions which imply the commutativity of a generalized periodic ring. |
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| ISSN: | 0161-1712 1687-0425 |