Correction to: Powers of the vertex cover ideals (Collect. Math. 65 (2014) 169–181)
نویسندگان
چکیده
We describe a combinatorial condition on graphwhich guarantees that all powers of its vertex cover ideal are componentwise linear. Then motivated by Eagon and Reiner’s Theorem we study whether the Cohen-Macaulay graph have linear free resolutions. After giving complete characterization cactus graphs (i.e., connected in which each edge belongs to at most one cycle) show their ideals
منابع مشابه
Symbolic Powers of Monomial Ideals and Vertex Cover Algebras
We introduce and study vertex cover algebras of weighted simplicial complexes. These algebras are special classes of symbolic Rees algebras. We show that symbolic Rees algebras of monomial ideals are finitely generated and that such an algebra is normal and Cohen-Macaulay if the monomial ideal is squarefree. For a simple graph, the vertex cover algebra is generated by elements of degree 2, and ...
متن کاملSymbolic Powers of Monomial Ideals and Vertex Cover Algebras
We introduce and study vertex cover algebras of weighted simplicial complexes. These algebras are special classes of symbolic Rees algebras. We show that symbolic Rees algebras of monomial ideals are finitely generated. Dedicated to Winfried Bruns on the occasion of his sixtieth birthday
متن کاملSymbolic Powers of Monomial Ideals and Vertex Cover Algebras
We introduce and study vertex cover algebras of weighted simplicial complexes. These algebras are special classes of symbolic Rees algebras. We show that symbolic Rees algebras of monomial ideals are finitely generated. Dedicated to Winfried Bruns on the occasion of his sixtieth birthday
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We develop tools to study the problem of containment of symbolic powers I(m) in powers I for a homogeneous ideal I in a polynomial ring k[P ] in N + 1 variables over an arbitrary algebraically closed field k. We obtain results on the structure of the set of pairs (r, m) such that I(m) ⊆ I. As corollaries, we show that I2 contains I(3) whenever S is a finite generic set of points in P2 (thereby ...
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An ideal K of R is a subset that is both a left ideal and a right ideal of R. For emphasis, we sometimes call it a two-sided ideal but the reader should understand that unless qualified, the word ideal will always refer to a two-sided ideal. The zero ideal (0) and the whole ring R are examples of two-sided ideals in any ring R. A (left)(right) ideal I such that I 6= R is called a proper (left)(...
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ژورنال
عنوان ژورنال: Collectanea Mathematica
سال: 2023
ISSN: ['2038-4815', '0010-0757']
DOI: https://doi.org/10.1007/s13348-023-00403-x