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 ?
Meera, Fuzzy soft prime ideals over right tenary near-rings, International Journal of Pure and Applied Mathematics, 85(3), 507-529, (2013).
where a runs over non-zero ideals in [O.sub.K], p runs over the prime ideals in [O.sub.K] and Na is the norm of a.
Among their topics are chains in semiprime and prime ideals in Leavitt path algebras, a category of extensions with endomorphism rings that have at most four maximal ideals, modules invariant under monomorphisms of their envelopes, rings in which every unit is a sum of a nilpotent and an idempotent, and direct sums of completely almost self-injective modules.` ([umlaut] Ringgold, Inc., Portland, OR)
Using this new definition, we proved many meaningful properties of nearly prime submodules which are similar to that of prime submodules and also prime ideals.
Rough prime ideals and rough fuzzy prime ideals in semigroups were proposed by Xiao and Zhang [17].
Prime ideals and primary ideals play a significant role in commutative ring theory.
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.
For every ideal I of R one has that the radical of I is the intersection of all prime ideals containing I.
We denote the family of all prime ideals of L by PI(L).
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. Chapter authors are scholars of mathematics in the US, Spain, China, and Iran.