Veronese Algebras and Modules of Rings with Straightening Laws

Details Veronese Algebras and Modules of Rings with Straightening Laws Veronese Algebras and Modules of Rings with Straightening Laws

2012-01-13

arxiv.org/abs/1201.2851v1

Mathematics

Commutative Algebra

14 pages; to appear in Journal of Commutative Algebra

Scientific paper

Do the Veronese rings of an algebra with straightening laws (ASL) still have an ASL structure? We give positive answers to this question in some particular cases, namely for the second Veronese algebra of Hibi rings and of discrete ASLs. We also prove that the Veronese modules of the polynomial ring have a structure of module with straightening laws. In dimension at most three we present a poset construction that has the required combinatorial properties to support such a structure.

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