Prime filtrations and Stanley decompositions of squarefree modules and Alexander duality |
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Authors: | Ali Soleyman Jahan |
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Institution: | 1.Department of Mathematics,University of Kurdistan,Sanandaj,Iran |
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Abstract: | In this paper we study how prime filtrations and squarefree Stanley decompositions of squarefree modules over the polynomial
ring and over the exterior algebra behave with respect to Alexander duality. The results which we obtained suggest a lower
bound for the regularity of a
\mathbb Zn{\mathbb {Z}^n}-graded module in terms of its Stanley decompositions. For squarefree modules this conjectured bound is a direct consequence
of Stanley’s conjecture on Stanley decompositions. We show that for pretty clean rings of the form R/I, where I is a monomial ideal, and for monomial ideals with linear quotient our conjecture holds. |
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