Identities of graded simple algebrasRepovš, Dušan (Avtor) Zaicev, Mikhail (Avtor) polynomial identitiesgraded algebrascodimensionsexponential growthWe study identities of finite dimensional algebras over a field of characteristic zero, graded by an arbitrary groupoid ▫$\Gamma$▫. First, we prove that its graded colength has a polynomially bounded growth. For any graded simple algebra ▫$A$▫, we prove the existence of the graded PI-exponent, provided that ▫$\Gamma$▫ is a commutative semigroup. If ▫$A$▫ is simple in a non-graded sense, the existence of the graded PI-exponent is proved without any restrictions on ▫$\Gamma$▫.20172019-09-13 13:38:36Članek v reviji110327sl