27 research outputs found
Complete normal forms for real hypersurfaces in at 2-nondegenerate points of Levi non-uniform rank zero
We construct complete normal forms for -dimensional real hypersurfaces in
which are -nondegenerate and also of Levi non-uniform rank
zero at the origin point . The latter condition means that the rank
of the Levi form vanishes at but not identically in a neighborhood of
it. The mentioned hypersurfaces are the only finitely nondegenerate real
hypersurfaces in for which their complete normal forms were
absent in the literature. As a byproduct, we also treat the underlying
biholomorphic equivalence problem between the hypersurfaces. Our primary
approach in constructing the desired complete normal forms is to utilize the
techniques derived in the theory of equivariant moving frames. It notably
offers the advantage of systematic and symbolic manipulation of the associated
computations.Comment: 32 p
Modules Satisfying the Prime Radical Condition and a Sheaf Construction for Modules I
The purpose of this paper and its sequel, is to introduce a new class of
modules over a commutative ring , called -radical modules
(modules satisfying the prime radical condition
"" for every prime ideal
, where is the
intersection of all prime submodules of containing ). This
class contains the family of primeful modules properly. This yields that over
any ring all free modules and all finitely generated modules lie in the class
of -radical modules. Also, we show that if is a domain (or a
Noetherian ring), then all projective modules are -radical. In
particular, if is an Artinian ring, then all -modules are
-radical and the converse is also true when is a Noetherian
ring. Also an -module is called -radical if
; for every maximal ideal
. We show that the two concepts
-radical and -radical are equivalent for all
-modules if and only if is a Hilbert ring. Semisimple
-radical (-radical) modules are also characterized. In
Part II we shall continue the study of this construction, and as an
application, we show that the sheaf theory of spectrum of -radical
modules (with the Zariski topology) resembles to that of rings.Comment: 18 Page