Rituximab and Combination Chemotherapy in Treating Patients With Non-Hodgkin's Lymphoma

DISEASE CHARACTERISTICS: * Histologically confirmed aggressive B-cell non-Hodgkin's lymphoma, including the following subtypes: * Grade 3 follicular lymphoma * Diffuse B-cell lymphoma, including diffuse large cell lymphoma with any of the following variants: * Centroblastic * Immunoblastic * Plasmablastic * Anaplastic large cell * T-cell-rich B-cell lymphoma * Primary effusion lymphoma * Intravascular B-cell lymphoma * Primary mediastinal B-cell lymphoma * Burkitt's or Burkitt-like lymphoma * Mantle cell lymphoma (blastoid) * Aggressive marginal zone lymphoma (monocytoid) * Previously untreated disease * CD20-positive disease * International Prognostic Index (IPI) score 0 * No bulky disease * Largest single or conglomerate tumor \< 7.5 cm in diameter * No mucosa-associated lymphoid tissue (MALT) lymphoma * No CNS involvement of lymphoma (intracerebral, meningeal, or intraspinal) PATIENT CHARACTERISTICS: * ECOG performance status 0-1 * Platelet count ≥ 100,000/mm\^3 * WBC ≥ 2,500/mm\^3 * Lactate dehydrogenase normal * Not pregnant or lactating * Fertile patients must use effective contraception during and for 1 year after study participation * Negative pregnancy test * No known hypersensitivity to the study medications * No known HIV-positivity * No active hepatitis infection * No impaired left ventricular function * No severe cardiac arrhythmias * No other impaired organ function * No other serious disorder * No other malignancy wit…