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