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 ?
Rumynin has defined the restricted universal enveloping algebra of a restricted Lie-Rinehart algebra L in the obvious way, and proved the corresponding Poincare-Birkhoff-Witt theorem in the case that L is projective: In a localization at a prime ideal, the restricted universal enveloping algebra is a free module with a PBW basis truncated at p-th powers.
upsilon]] := [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] if [upsilon] is the prime defined by a prime ideal p of [O.
In Section 5 we advance the fuzzy prime ideal and fuzzy strong prime ideal in prelinear coresiduated lattices.
An ideal P of an LA-semigroup S with left identity e is called prime ideal if AB [subset or equal to] P implies either
In this paper we define a notion of weakly prime ideal in near-ring (not necessarily commutative).
Separation: Every prime ideal [Mathematical Expression Omitted] generates a prime ideal of analytic functions [Mathematical Expression Omitted].
Note that every ideal of a BCK-algebra is a down-set and every prime ideal is a prime-set.
This construction makes sense for any prime ideal in place of the maximal ideal [M.
Let 1 be the prime ideal of F' dividing l, and [lambda] an algebraic integer in F' generating the principal ideal 1.
An ideal p [subset] R generated by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a minimal prime ideal of I(G) if and only if C is a minimal vertex cover for G.
In this paper, we study the remaining parts, namely, we give such bounds for modular forms with Fourier coefficients in an arbitrary algebraic number field K and for any prime ideal p in K.
Less obvious to see is that if L is not pseudocompact, then not only does R x L have a free maximal ideal, it actually also has a free non-maximal prime ideal (Proposition 3.