Linear resolutions over Koszul complexes and Koszul homology algebras

Let R be a standard graded commutative algebra over field k , let K its Koszul complex viewed as differential -algebra, and H the homology of . This paper studies interplay between homological properties three algebras In particular, we introduce two definitions Koszulness that extend familiar property originally introduced by Priddy: one which applies to (and, more generally, any connected -algebra) other, called strand-Koszulness The main theoretical result is complete description how these are related each other. shows stronger than include examples classes have strand-Koszul.