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Given an artin algebra with an idempotent element we compare the algebras and with respect to Gorensteinness, singularity categories and the finite generation condition for the Hochschild cohomology. In particular, we identify assumptions on the idempotent element which ensure that is Gorenstein if and only if is Gorenstein, that the singularity categories of and are equivalent and that holds for if and only if holds for . We approach the problem by using recollements of abelian categories and we prove the results concerning Gorensteinness and singularity categories in this general setting. The results are applied to stable categories of Cohen–Macaulay modules and classes of triangular matrix algebras and quotients of path algebras. References