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Given an artin algebra $\Lambda$ with an idempotent element $a$ we comparethe algebras $\Lambda$ and $a\Lambda a$ with respect to Gorensteinness,singularity categories and the finite generation condition Fg for theHochschild cohomology. In particular, we identify assumptions on the idempotentelement $a$ which ensure that $\Lambda$ is Gorenstein if and only if $a\Lambdaa$ is Gorenstein, that the singularity categories of $\Lambda$ and $a\Lambda a$are equivalent and that Fg holds for $\Lambda$ if and only if Fg holds for$a\Lambda a$. We approach the problem by using recollements of abeliancategories and we prove the results concerning Gorensteinness and singularitycategories in this general setting. The results are applied to stablecategories of Cohen-Macaulay modules and classes of triangular matrix algebrasand quotients of path algebras.

Gorenstein categories, singular equivalences and finite generation of cohomology rings in recollements