Complex sentence: An ultraproduct is a mathematical construction, a generalization of the ultrapower (defined below), which is used in abstract algebra to construct new fields from given ones, and in model theory, a branch of mathematical logic.
Split into simpler sentences: An ultraproduct is a mathematical construction, of which the ultrapower (defined below) is a special case. Ultraproducts are useds used in abstract algebra to construct new fields from given ones, and in model theory, a branch of mathematical logic.