Mircea Cimpoeaş
Abstract
We prove that if $I$ is a monomial ideal with linear quotients in a ring of polynomials $S$ in $n$ indeterminates and depth$(S/I)=n-2$, then sdepth$(S/I)=n-2$. Also, we prove that sdepth$(S/I)\geq {\rm depth}(S/I)$ for a monomial ideal $I$ with linear quotients which satisfies certain technical conditions.
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We prove that if $I$ is a monomial ideal with linear quotients in a ring of polynomials $S$ in $n$ indeterminates and depth$(S/I)=n-2$, then sdepth$(S/I)=n-2$. Also, we prove that sdepth$(S/I)\geq {\rm depth}(S/I)$ for a monomial ideal $I$ with linear quotients which satisfies certain technical conditions.
Key concepts: Monomial, Monomial ideal, Quotient, Mathematics, Ideal (ethics), Polynomial ring, Pure mathematics, Ring (chemistry)