Results on the behavior of the Ratliff–Rush operation and the depth of the associated graded ring
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DOI: 10.1080/00927872.2021.1897989
Abstract: Abstract We give a full characterization of the unique Ratliff–Rush complete ideals in the polynomial rings R with two variables over a field. For a class of monomial ideals in R, we investigate the Ratliff–Rush… read more here.
Keywords: associated graded; graded ring; rush; results behavior ... See more keywords
On the associated graded ring of semigroup algebras
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DOI: 10.1080/00927872.2023.2203773
Abstract: In this paper, we give the necessary and sufficient conditions for the Cohen-Macaulayness of the associated graded ring of a simplicial affine semigroups using Gr\"{o}bner basis. We generalize the concept of homogeneous numerical semigroup for… read more here.
Keywords: associated graded; semigroup algebras; graded ring; simplicial affine ... See more keywords