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Prime ideal

From Encyclopedia of Mathematics
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A two-sided ideal of a ring such that the inclusion for any two-sided ideals and of implies that either or . An ideal of a ring is prime if and only if the set is an -system, i.e. for any there exists an such that . An ideal of a ring is prime if and only if the quotient ring by it is a prime ring.


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References

[a1] L.H. Rowen, "Ring theory" , I , Acad. Press (1988) pp. 163
How to Cite This Entry:
Prime ideal. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Prime_ideal&oldid=29171
This article was adapted from an original article by K.A. Zhevlakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article