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We define polynomial H-identities for comodule algebras over a Hopf algebra Hand establish general properties for the corresponding T-ideals. In the case His a Taft algebra or the Hopf algebra E(n), we exhibit a finite set ofpolynomial H-identities which distinguish the Galois objects over H up toisomorphism.

Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebras