Abstract
This article establishes a concrete relation between order ideals of minimal generators and annihilator ideals. For a regular local ring $R$ and ideal $I$ the authors construct an $R$-module $M$ with minimal generator having $I$ as order ideal. Further, it is shown that most variability in ideal–theoretic behavior of such order ideals is exhibited by modules of projective dimension~one. The authors ``introduce'' the concept of $*$-orthogonality and use their syzygy theorem to show constraints on the size and height of a $*$-orthogonal set in a given finitely generated non-free module. The paper contains an application of the theory of order ideals to the binomial behavior of syzygy rank.
Citation
E. Graham Evans. Phillip Griffith. "Order ideals, annihilator ideals and pathological behavior." J. Commut. Algebra 8 (1) 43 - 59, 2016. https://doi.org/10.1216/JCA-2016-8-1-43
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