  We study absolutely Koszul algebras, Koszul algebras with the Backelin-Roos
property and their behavior under standard algebraic operations. In particular,
we identify some Veronese subrings of polynomial rings that have the
Backelin-Roos property and conjecture that the list is indeed complete. Among
other things, we prove that every universally Koszul ring defined by monomials
has the Backelin-Roos property.
