Lattices of Annihilators in Commutative Algebras Over Fields

Abstract

Let K be any field and L be any lattice. In this note we show that L is a sublattice of annihilators in an associative and commutative K-algebra. If L is finite, then our algebra will be finite dimensional over K.

Keywords

• poset
• lattice
• annihilator
• contracted semigroup algebra
• finite dimensional algebra