Numerical invariants of identities of unital algebras
  We study polynomial identities of algebras with adjoined external unit. For a wide class of algebras we prove that adjoining external unit element leads to increasing of PI-exponent precisely to 1. We also show that any real number from the interval [2,3] can be realized as PI-exponent of some unital algebra. 
Du\v{s}an Repov\v{s}, Mikhail Zaicev
math.RA