Some conditions for finiteness of a ring
Extending a result of Putcha and Yaqub, we prove that a non-nil ring must be finite if it has both ascending chain condition and descending chain condition on non-nil subrings. We also prove that a periodic ring with only finitely many non-central zero divisors must be either finite or commutative.
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| Format: | Article |
| Language: | English |
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Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171288000286 |
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| _version_ | 1832554630343557120 |
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| author | Howard E. Bell |
| author_facet | Howard E. Bell |
| author_sort | Howard E. Bell |
| collection | DOAJ |
| description | Extending a result of Putcha and Yaqub, we prove that a non-nil ring must be finite if it has both ascending chain condition and descending chain condition on non-nil subrings. We also prove that a periodic ring with only finitely many non-central zero divisors must be either finite or commutative. |
| format | Article |
| id | doaj-art-417b429262b94492abff2a85a4bd78b4 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1988-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-417b429262b94492abff2a85a4bd78b42025-02-03T05:51:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-0111223924210.1155/S0161171288000286Some conditions for finiteness of a ringHoward E. Bell0Department of Mathematics, Brock University, St. Catharines, Ontario L2S 3A1, CanadaExtending a result of Putcha and Yaqub, we prove that a non-nil ring must be finite if it has both ascending chain condition and descending chain condition on non-nil subrings. We also prove that a periodic ring with only finitely many non-central zero divisors must be either finite or commutative.http://dx.doi.org/10.1155/S0161171288000286finiteness of ringsperiodic ringscommutativity. |
| spellingShingle | Howard E. Bell Some conditions for finiteness of a ring International Journal of Mathematics and Mathematical Sciences finiteness of rings periodic rings commutativity. |
| title | Some conditions for finiteness of a ring |
| title_full | Some conditions for finiteness of a ring |
| title_fullStr | Some conditions for finiteness of a ring |
| title_full_unstemmed | Some conditions for finiteness of a ring |
| title_short | Some conditions for finiteness of a ring |
| title_sort | some conditions for finiteness of a ring |
| topic | finiteness of rings periodic rings commutativity. |
| url | http://dx.doi.org/10.1155/S0161171288000286 |
| work_keys_str_mv | AT howardebell someconditionsforfinitenessofaring |