T-duality and Noncommutative DBI Action

In this article we study the noncommutative description of the DBI Lagrangian and its T-dual counterpart. We restrict the freedoms of the noncommutativity parameters of these Lagrangians. Therefore the noncommutativity parameter, the effective metric, the effective coupling constant of the string and the extra modulus ${\tilde \Phi}$ of the effective T-dual theory, can be expressed in terms of the closed string variables $g$, $B$, $g_s$ and the noncommutativity parameter of the effective theory of open string.