Study of Gorenstein algebras

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We extended Serre duality theory in algebraic geometry to Noether algebras and, using this notion, we characterized Gorensteinness of Noether algebras and provided a necessary and sufficient condition for a tilting complex over a Gorenstein algebra to have a Gorenstein algebra as an endomorphism algebra. Here, a Noether algebra is a module-finite algebra over a commutative Noether ring and is said to be a Gorenstein algebra if its dual over a Gorenstein base ring in the derived category is a shifted projective generator.