Stanley depth of monomial ideals with small number of generators

Mathematics – Commutative Algebra

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

7 pages. submitted to Central European Journal of Mathematics

Scientific paper

For a monomial ideal $I\subset S=K[x_1,...,x_n]$, we show that $\sdepth(S/I)\geq n-g(I)$, where $g(I)$ is the number of the minimal monomial generators of $I$. If $I=vI'$, where $v\in S$ is a monomial, then we see that $\sdepth(S/I)=\sdepth(S/I')$. We prove that if $I$ is a monomial ideal $I\subset S$ minimally generated by three monomials, then $I$ and $S/I$ satisfy the Stanley conjecture. Given a saturated monomial ideal $I\subset K[x_1,x_2,x_3]$ we show that $\sdepth(I)=2$. As a consequence, $\sdepth(I)\geq \sdepth(K[x_1,x_2,x_3]/I)+1$ for any monomial ideal in $I\subset K[x_1,x_2,x_3]$.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Stanley depth of monomial ideals with small number of generators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Stanley depth of monomial ideals with small number of generators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stanley depth of monomial ideals with small number of generators will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-522467

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.