Advanced studies in pure mathematics· 2018Q3
Distributive Lattices, Affine Semigroup Rings and Algebras with Straightening Laws
- 199citations
- Q3SCImago
- 2018year
Short summary
All finite distributive lattices are integral over a field k, meaning they can be represented by a homogeneous algebra with straightening laws (ASL) domain.
AI-generated from the title and abstract; the full text is not read.
Key points
- Finite distributive lattices are integral over a field k.
- Integrality is established via representation as a homogeneous ASL domain.
- The proof relies on Birkhoff's fundamental structure theorem for lattices.
AI-generated from the title and abstract; the full text is not read.
Abstract
A lattice L is called integral over a field k if there exists a homogeneous ASL (algebra with straightening laws) domain on Lover k.By virtue of fundamental structure theorem of Birkhoff, we can prove that every finite distributive lattice is integral.
The authors' abstract, as published at the source. Advanced studies in pure mathematics, 2018 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics