large ideal

An ideal $I$ of a ring $R$ is called a large ideal if for every ideal $J$ of $R$ such that $J\eq\\{0\\}$ , $I\\cap J\eq\\{0\\}$

A ring is semiprime iff every large ideal is dense.

Obviously all nontrivial ideal of an integral domain is a large ideal, and the maximal ideal of any non-trivial local ring is a large ideal.

References

1 N.J. Fine, L. Gillman, J. Lambek,”Rings of Quotients of Rings of Functions”,
Transcribed and edited into PDF from the original 1966 McGill University Press book
(see http://tinyurl.com/24unqshere, Editors: M. Barr, R. Raphael),
http://tinyurl.com/ytw3tjOnline download,Accessed 24.10.2007

单词	LargeIdeal
释义	large ideal An ideal $I$ of a ring $R$ is called a large ideal if for every ideal $J$ of $R$ such that $J\eq\\{0\\}$ , $I\\cap J\eq\\{0\\}$ A ring is semiprime iff every large ideal is dense. Obviously all nontrivial ideal of an integral domain is a large ideal, and the maximal ideal of any non-trivial local ring is a large ideal. References 1 N.J. Fine, L. Gillman, J. Lambek,”Rings of Quotients of Rings of Functions”, Transcribed and edited into PDF from the original 1966 McGill University Press book (see http://tinyurl.com/24unqshere, Editors: M. Barr, R. Raphael), http://tinyurl.com/ytw3tjOnline download,Accessed 24.10.2007
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