141 research outputs found
Around general neron desingularization
It gives some new forms of General Neron Desingularization and new
applications.Comment: It simplifies the proof of Theorem 1
A method to compute the General Neron Desingularization in the frame of one dimensional local domains
An algorithmic proof of General Neron Desingularization is given here for one
dimensional local domains and it is implemented in \textsc{Singular}. Also a
theorem recalling Greenberg' strong approximation theorem is presented for one
dimensional Cohen-Macaulay local rings.Comment: In this version some examples were added and many misprints were
corrected especially from the last sectio
Nested Artin approximation
A short proof of the linear nested Artin approximation property of the
algebraic power series rings is given here.Comment: We simplified the statements of proposition
Stanley conjecture on intersections of four monomial prime ideals
We show that the Stanley's Conjecture holds for an intersection of four
monomial prime ideals of a polynomial algebra over a field and for an
arbitrary intersection of monomial prime ideals of such
that for all .Comment: accepted to Communications in Algebr
Simple General Neron Desingularization in local -algebras
In this form will appear in Communications in Algebra.Comment: Proposition 5 was extended and a sketh proof is include
Stanley depth of monomial ideals
Let be two monomial ideals of a polynomial algebra over a
field generated in degree , resp. . We study when the
Stanley Conjecture holds for using the recent result of \cite{IKM}
concerning the polarization
On the Bass-Quillen Conjecture and Swan's question
We present a question which implies a complete positive answer for the
Bass-Quillen Conjecture.Comment: In this form will appear in Combinatorial Structures in Algebra and
Geometry, Editors Dumitru Stamate, Thomasz Szemberg, Springer Proceedings in
Mathematics and Statistics Series, 202
Upper bounds of depth of monomial ideals
Let be two ideals of a polynomial ring over a field,
generated by square free monomials.
We show that some inequalities among the numbers of square free monomials of
of different degrees give upper bounds of \depth_SI/J
Depth of factors of square free monomial ideals
Let be an ideal of a polynomial algebra over a field, generated by
square free monomials of degree . If is bigger (or equal, if is not
principal) than the number of square free monomials of of degree ,
then \depth_SI= d. Let , be generated by square
free monomials of degree . If is bigger than the number of square
free monomials of of degree , or more generally the Stanley
depth of is , then \depth_SI/J= d. In particular, Stanley's
Conjecture holds in theses cases
Depth and minimal number of generators of square free monomial ideals
Let be an ideal of a polynomial algebra over a field generated by
square free monomials of degree . If contains more monomials of
degree than of the total number of square free monomials of
of degree then \depth_SI\leq d, in particular the Stanley's
Conjecture holds in this case
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