Algebras with Straightening Laws

Algebras with Straightening Law (or ASLs) were introduced by Eisenbud, DeConcini, and Procesi as a means of studying homological properties of determinantal varieties. After giving the definition of an ASL and presenting some examples, I will demonstrate how a commutative algebraist might use the fact that an algebra is an ASL to check if it is Cohen-Macaulay (a very desirable property) using simple poset properties.