Connected sums of graded Artinian Gorenstein algebras and Lefschetz properties

In their paper [1], H. Ananthnarayan, L. Avramov, and W.F. Moore introduced a connected sum construction for local Gorenstein rings A,B over ring T, which, in the graded Artinian case, can be viewed as an algebraic analogue of topological same name. We give two alternative descriptions this sum: first uses analogues Thom classes vector bundles Gysin homomorphisms, second is terms Macaulay dual generators. also investigate extent to which algebra T preserves weak or strong Lefschetz property, thus providing new satisfy these properties.