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.