Noncommutativity and noncentral zero divisors
Let R be a ring, Z its center, and D the set of zero divisors. For finite noncommutative rings, it is known that D\Z≠∅. We investigate the size of |D\Z| in this case and, also, in the case of infinite noncommutative rings with D\Z≠∅.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171299220674 |
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| _version_ | 1832564172811927552 |
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| author | Howard E. Bell Abraham A. Klein |
| author_facet | Howard E. Bell Abraham A. Klein |
| author_sort | Howard E. Bell |
| collection | DOAJ |
| description | Let R be a ring, Z its center, and D the set of zero divisors. For finite noncommutative rings, it is known that D\Z≠∅. We investigate the size of |D\Z| in this case and, also, in the case of infinite noncommutative rings with D\Z≠∅. |
| format | Article |
| id | doaj-art-152947b08b864707850b66cd77035d4e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-152947b08b864707850b66cd77035d4e2025-02-03T01:11:38ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251999-01-01221677410.1155/S0161171299220674Noncommutativity and noncentral zero divisorsHoward E. Bell0Abraham A. Klein1Department of Mathematics, Brock University, ST. Catharines, Ontario, L2S 3A1, CanadaSackler Faculty of Exact Sciences, School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, IsraelLet R be a ring, Z its center, and D the set of zero divisors. For finite noncommutative rings, it is known that D\Z≠∅. We investigate the size of |D\Z| in this case and, also, in the case of infinite noncommutative rings with D\Z≠∅.http://dx.doi.org/10.1155/S0161171299220674Finite noncommutative ringsinfinite noncommutative ringscentral and noncentral zero divisors. |
| spellingShingle | Howard E. Bell Abraham A. Klein Noncommutativity and noncentral zero divisors International Journal of Mathematics and Mathematical Sciences Finite noncommutative rings infinite noncommutative rings central and noncentral zero divisors. |
| title | Noncommutativity and noncentral zero divisors |
| title_full | Noncommutativity and noncentral zero divisors |
| title_fullStr | Noncommutativity and noncentral zero divisors |
| title_full_unstemmed | Noncommutativity and noncentral zero divisors |
| title_short | Noncommutativity and noncentral zero divisors |
| title_sort | noncommutativity and noncentral zero divisors |
| topic | Finite noncommutative rings infinite noncommutative rings central and noncentral zero divisors. |
| url | http://dx.doi.org/10.1155/S0161171299220674 |
| work_keys_str_mv | AT howardebell noncommutativityandnoncentralzerodivisors AT abrahamaklein noncommutativityandnoncentralzerodivisors |