Task: Text Categorization
Input (English): Euler's proof of Fermat's Last Theorem for the n equals 3 case involved extending integer arithmetic to one of these structures, which contain numbers of the form a plus b times the square root of negative 3. Dedekind defined an ideal complex number based upon a property related to these structures and Hilbert utilized (*) polynomial ones to solve his Basis Theorem. The advent of quaternion algebra and the extension of the axioms of this structure to square matrices led to the formulation of its non-commutative theory and the first single theory of the abstract commutative variety of these structures was proposed by Noether. FTP, what are these mathematical objects defined as a set containing two operators that satisfy a collection of axioms.
Output (English): Science