Prime ideal
From Encyclopedia of Mathematics
Revision as of 21:49, 11 December 2012 by Remag12 (talk | contribs) (→Comments: about m system ststement)
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.
Comments
This assumes that the empty set is an m system by default.
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
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