Two-sided essential nilpotence
An ideal I of a ring A is essentially nilpotent if I contains a nilpotent ideal N of A such that J⋂N≠0 whenever J is a nonzero ideal of A contained in I. We show that each ring A has a unique largest essentially nilpotent ideal EN(A). We study the properties of EN(A) and, in particular, we investiga...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1992-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171292000449 |
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Article |
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doaj-480f7afe8380460bace7c20e388253ef2020-11-24T23:08:36ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-0115235135410.1155/S0161171292000449Two-sided essential nilpotenceEsfandiar Eslami0Patrick Stewart1Department of Mathematics, University of Kerman, Kerman, IranDepartment of Mathematics, Dalhousie University, Nova Scotia, Halifax B3H 3J5, CanadaAn ideal I of a ring A is essentially nilpotent if I contains a nilpotent ideal N of A such that J⋂N≠0 whenever J is a nonzero ideal of A contained in I. We show that each ring A has a unique largest essentially nilpotent ideal EN(A). We study the properties of EN(A) and, in particular, we investigate how this ideal behaves with respect to related rings.http://dx.doi.org/10.1155/S0161171292000449essential idealnilpotent idealfree normalizing extensioncrossed productMorita equivalentfixed ring. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Esfandiar Eslami Patrick Stewart |
| spellingShingle |
Esfandiar Eslami Patrick Stewart Two-sided essential nilpotence International Journal of Mathematics and Mathematical Sciences essential ideal nilpotent ideal free normalizing extension crossed product Morita equivalent fixed ring. |
| author_facet |
Esfandiar Eslami Patrick Stewart |
| author_sort |
Esfandiar Eslami |
| title |
Two-sided essential nilpotence |
| title_short |
Two-sided essential nilpotence |
| title_full |
Two-sided essential nilpotence |
| title_fullStr |
Two-sided essential nilpotence |
| title_full_unstemmed |
Two-sided essential nilpotence |
| title_sort |
two-sided essential nilpotence |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1992-01-01 |
| description |
An ideal I of a ring A is essentially nilpotent if I contains a nilpotent ideal N of A such that J⋂N≠0 whenever J is a nonzero ideal of A contained in I. We show that each ring A has a unique largest essentially nilpotent ideal EN(A). We study the properties of EN(A) and, in particular, we investigate how this ideal behaves with respect to related rings. |
| topic |
essential ideal nilpotent ideal free normalizing extension crossed product Morita equivalent fixed ring. |
| url |
http://dx.doi.org/10.1155/S0161171292000449 |
| work_keys_str_mv |
AT esfandiareslami twosidedessentialnilpotence AT patrickstewart twosidedessentialnilpotence |
| _version_ |
1725613359136505856 |