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- W2894637448 abstract "For an arbitrary ideal $I$ in a polynomial ring $R$ we define the notion of initially regular sequences on $R/I$. These sequences share properties with regular sequences. In particular, the length of an initially regular sequence provides a lower bound for the depth of $R/I$. Using combinatorial information from the initial ideal of $I$ we construct sequences of linear polynomials that form initially regular sequences on $R/I$. We identify situations where initially regular sequences are also regular sequences, and we show that our results can be combined with polarization to improve known depth bounds for general monomial ideals." @default.
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- W2894637448 date "2018-10-02" @default.
- W2894637448 modified "2023-09-27" @default.
- W2894637448 title "Initially regular sequences and depths of ideals" @default.
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