Shellability of semigroup rings

Abstract

The concepts of $\Lambda$-shellability of locally finite posets as well as of extendable sequentially Koszul algebras will be introduced. It will be proved that the divisor poset of a homogeneous semigroup ring is $\Lambda$-shellable if and only if the semigroup ring is extendable sequentially Koszul. Examples of extendable sequentially Koszul semigroup rings contain all monomial ASL's (algebras with straightening laws) and all second squarefree Veronese subrings.