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Algebra retracts of monomial cut algebras
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Let [Formula: see text] be a subgraph and [Formula: see text] be a minor of a simple graph [Formula: see text]. For any field [Formula: see text], we prove that [Formula: see text] and [Formula: see text] are algebra retracts of [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are monomial cut algebras of the graph [Formula: see text], [Formula: see text] and [Formula: see text], respectively. Moreover, for the complete graph [Formula: see text], we give an upper bound of the Castelnuovo–Mumford regularity of the monomial cut ideal [Formula: see text]
Title: Algebra retracts of monomial cut algebras
Description:
Let [Formula: see text] be a subgraph and [Formula: see text] be a minor of a simple graph [Formula: see text].
For any field [Formula: see text], we prove that [Formula: see text] and [Formula: see text] are algebra retracts of [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are monomial cut algebras of the graph [Formula: see text], [Formula: see text] and [Formula: see text], respectively.
Moreover, for the complete graph [Formula: see text], we give an upper bound of the Castelnuovo–Mumford regularity of the monomial cut ideal [Formula: see text].
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