Annihilators of nilpotent elements
Let x be a nilpotent element of an infinite ring R (not necessarily with 1). We prove that A(x)—the two-sided annihilator of x—has a large intersection with any infinite ideal I of R in the sense that card(A(x)∩I)=cardI. In particular, cardA(x)=cardR; and this is applied to prove that if N is the se...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.3517 |
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| _version_ | 1832549010913624064 |
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| author | Abraham A. Klein |
| author_facet | Abraham A. Klein |
| author_sort | Abraham A. Klein |
| collection | DOAJ |
| description | Let x be a nilpotent element of an infinite ring R (not necessarily with 1). We prove that A(x)—the two-sided annihilator of x—has a large intersection with any infinite ideal I of R in the sense that card(A(x)∩I)=cardI. In particular, cardA(x)=cardR; and this is applied to prove that if N is the set of nilpotent elements of R and R≠N, then card(R\N)≥cardN. |
| format | Article |
| id | doaj-art-248f665640a44d2891bdd9da5e67048a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-248f665640a44d2891bdd9da5e67048a2025-02-03T06:12:19ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005213517351910.1155/IJMMS.2005.3517Annihilators of nilpotent elementsAbraham A. Klein0Department of Pure Mathematics, School of Mathematical Sciences, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, IsraelLet x be a nilpotent element of an infinite ring R (not necessarily with 1). We prove that A(x)—the two-sided annihilator of x—has a large intersection with any infinite ideal I of R in the sense that card(A(x)∩I)=cardI. In particular, cardA(x)=cardR; and this is applied to prove that if N is the set of nilpotent elements of R and R≠N, then card(R\N)≥cardN.http://dx.doi.org/10.1155/IJMMS.2005.3517 |
| spellingShingle | Abraham A. Klein Annihilators of nilpotent elements International Journal of Mathematics and Mathematical Sciences |
| title | Annihilators of nilpotent elements |
| title_full | Annihilators of nilpotent elements |
| title_fullStr | Annihilators of nilpotent elements |
| title_full_unstemmed | Annihilators of nilpotent elements |
| title_short | Annihilators of nilpotent elements |
| title_sort | annihilators of nilpotent elements |
| url | http://dx.doi.org/10.1155/IJMMS.2005.3517 |
| work_keys_str_mv | AT abrahamaklein annihilatorsofnilpotentelements |