Let A —> B be a ring map such that B ⊗_{A} B —> B is flat. Let N be a B-module. If N is flat as an A-module, then N is flat as a B-module. See Tag Tag 092C.

_{A} B —> B is flat. Let N be a B-module. If N is flat as an A-module, then N is flat as a B-module. See Tag Tag 092C.