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We propose a definition of Gorenstein Differential Graded Algebra. In order to give examples, we introduce the technical notion of Gorenstein morphism. This enables us to prove the following:

Theorem:Let A be a noetherian local commutative ring, let L be a bounded complex of finitely generated projective A-modules which is not homotopy equivalent to zero, and let ɛ=Hom _A (L, L)be the endomorphism Differential Graded Algebra of L. Then ɛ is a Gorenstein Differential Graded Algebra if and only if A is a Gorenstein ring.

Theorem:Let A be a noetherian local commutative ring with a sequence of elements a=(a ₁,…,a _n )in the maximal ideal, and let K(a)be the Koszul complex of a.Then K(a)is a Gorenstein Differential Graded Algebra if and only if A is a Gorenstein ring.

Theorem:Let A …