Which greenhouse gas is emitted from decomposing trash?

It depends on how the trash decomposes. If it is being consumed by aerobic bacteria (oxygen needing) it is likely carbon dioxide (CO2). If the trach is decomposed by anaerobic bacteria (non oxygen metabolism) it is lekely methane (CH4). If eathen by termires and such is is methane again. In all cased there is some water (H2O) emitted, another greenhouse gas.