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.

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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.

A note on the restricted universal enveloping algebra of a restricted Lie-Rinehart Algebra

upsilon]] := [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] if [upsilon] is the prime defined by a prime ideal p of [O.

Balancing non-Wieferich primes in arithmetic progression and abc conjecture

In Section 5 we advance the fuzzy prime ideal and fuzzy strong prime ideal in prelinear coresiduated lattices.

Characterizations of fuzzy ideals in 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

Neutrosophic left almost semigroup

In this paper we define a notion of weakly prime ideal in near-ring (not necessarily commutative).

Weakly prime ideals in near-rings

Separation: Every prime ideal [Mathematical Expression Omitted] generates a prime ideal of analytic functions [Mathematical Expression Omitted].

Approximation in compact Nash manifolds

Note that every ideal of a BCK-algebra is a down-set and every prime ideal is a prime-set.

A class of special subsets of a BCK-algebra

This construction makes sense for any prime ideal in place of the maximal ideal [M.

Algebraic reduction and rigidity for Hilbert modules

Let 1 be the prime ideal of F' dividing l, and [lambda] an algebraic integer in F' generating the principal ideal 1.

Non-norm-euclidean fields in basic [Z.sub.l]-extensions

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.

Theoretic properties of the symmetric algebra of edge ideals

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.

Remark on Sturm bounds for Siegel modular forms of degree 2

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.