(Gorenstein) silting modules in recollements

In the paper, we focus on the silting properties and the combinatorial properties of silting and Gorenstein, which is called Gorenstein silting, where the main tools used are recollements of module categories and tensor products. For a ring A and its idempotent ideal J, we show that an A/J-module T is a silting A-module if and only if T is a silting A/J-module. For the finite dimensional k-algebras, with k a field, we show that the tensor products of silting modules are still silting. We also show that the (partial) Gorenstein silting properties can be glued by the recollements of module categories of Noetherian rings. As a consequence, we glue the Gorenstein silting modules of an upper triangular matrix Gorenstein ring by those of the involved rings.