prime ideal

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prime ideal

[′prīm ī′dēl]
(mathematics)
A principal ideal of a ring given by a single element that has properties analogous to those of the prime numbers.
References in periodicals archive ?
K] (a, b, c) is the set of all prime ideals p of [O.
In Section 4 we introduce the concepts of fuzzy prime ideals and fuzzy strong prime ideals in coresiduated lattices and obtain some of their characterizations.
Specific topics covered include characterization of almost injective modules, minimal prime ideals and quasi-duo rings.
For every ideal I of R one has that the radical of I is the intersection of all prime ideals containing I.
An LA-semigroup S is called fully prime LA-semigroup if all of its ideals are prime ideals.
For x [member of] N, < x > denote the ideal of N generated by x, and P (N) denotes the intersection of all prime ideals of N.
Chapters consider local and reduced rings, and commutative rings in general, as well as the classification of minimal ring extensions, linear systems theory over commutative rings, and the history and summary of asymptotic stability of associated or attached prime ideals.
Since T is weakly Prime, we On Prime, Weakly Prime Ideals in Semigroups 3 have AB [subset or equal to] [AB) [subset or equal to] T or BA [subset or equal to] [BA) [subset or equal to] T, A [subset or equal to] T or B [subset or equal to] T
1]), by taking inverse images of graded prime ideals, see [2] and [15].
These two ideals are proper real prime ideals and q lies over p; put [Mathematical Expression Omitted].
I] is a radical ideal and hence equals the intersection of all prime ideals of R([beta]L) containing it.