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We consider when the product of two Toeplitz operators with some quasihomogeneous symbols on the Bergman space of the unit ball equals a Toeplitz operator with quasihomogeneous symbols. We also characterize finite-rank semicommutators or commutators of two Toeplitz operators with quasihomogeneous symbols.doi:10.1155/2012/414201 fatcat:npi6k2gd6fe5zfqewaytcezj34