Several inequalities regarding sdepth

Abstract

We give several bounds for $sdept{h}_S(I+J)$, $sdept{h}_S(I\cap J)$, $sdept{h}_S(S/(I+J))$, $sdept{h}_S(S/(I\cap J))$, $sdept{h}_S(I:J)$ and $sdept{h}_S(S/(I:J))$ where $I,J\subset S=K[x_1,...,x_n]$ are monomial ideals. Also, we give several equivalent forms of Stanley Conjecture for $I$ and $S/I$, where $I\subset S$ is a monomial ideal.

13 pages

References in corpus (3)

• An inequality between depth and Stanley depth
• Stanley depth of monomial ideals with small number of generators
• Special Stanley Decompositions