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Let R and S be commutative rings, let J be an ideal of S and let f: R→ S be a ring homomorphism. In this paper, we investigate some homological properties of the amalgamation of R with S along J with respect to f (denoted by R⊳⊲ f J), introduced by D’Anna and Fontana in 2007. In addition, we deal with the strongly cotorsion properties of local cohomology module of R⊳⊲ f J, when R⊳⊲ f J is a local Noetherian ring.