We develop a procedure to reproduce the ten-dimensional generalized supergravity equations from T-duality covariant equations that facilitates generalization to U-duality covariant formulations of eleven-dimensional supergravity. The latter leads to a modification of the eleven-dimensional supergravity equations with terms that contain a rank-2 tensor field, which is the eleven-dimensional analog of the nonunimodularity Killing vector in ten dimensions.
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