those included in the regression of interest (W) and the instruments (Z) Reduced homology, a minor modification made to homology theory in algebraic topology, designed to make a point have all its homology groups zero Reduced product, a construction that generalizes both direct product and ultraproduct Reduced residue system, a set of φ(n) integers such that each integer is relatively prime to n and no two are congruent modulo n Reduced ring, a ring with no non-zero nilpotent elements Reduced row echelon form, a certain reduced row echelon form of a matrix which completely and uniquely determines its row space Reduced word, in a free group, a word with no adjacent generator-inverse pairs Medicine Medical procedures Lung volume reduction surgery, a treatment for chronic obstructive pulmonary disease Selective reduction (or fetal reduction), the practice of reducing the number of fetuses in a multifetal pregnancy Reduction (orthopedic surgery), a medical procedure to restore a fracture or dislocation to the correct alignment Ventricular reduction, a type of operation in cardiac surgery Cosmetic surgery: Breast reduction Jaw reduction Other uses in medicine Weight loss In epidemiology: Relative risk reduction, the absolute risk reduction by the control event rate Absolute risk reduction, the decrease in risk of a given activity or treatment in relation to a control activity or treatment Urea reduction ratio (URR), a dimensionless number used to quantify hemodialysis treatment adequacy Physics Dimensional reduction, the limit of a compactified theory where the size of the compact dimension goes to zero Reduction criterion, in quantum information theory, a necessary condition a mixed state must satisfy in order for it to be separable Reduced mass, the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics Reduced properties (pressure, temperature, or volume) of a fluid, defined based on the fluid's critical point Other uses in science and technology Lithic reduction, in Stone Age toolmaking, to detach lithic flakes from a lump of tool stone Noise reduction, in acoustic or signal processing Reduction drive, a mechanical device to shift rotational speed Arts and media Reducing (film), a 1931 American film Reduction (music), music arranged for smaller resources (piano) for easier analysis or performance Linguistics Accent reduction, modifying one's foreign accent towards that of a native speaker Vowel reduction, any change in vowel quality perceived as "weakening" Vowel reduction in English Relaxed pronunciation, slurring of syllables of common words Definite article reduction, use of vowel-less