Task: Text Categorization
Input (English): The category of these objects has the property that every morphism is a monomorphism. The spectrum of one of these objects contains one point, and the p-adic numbers for a given p form one of these. These objects necessarily have zero Krull dimension. Those with a finite number of elements have order equal to a power of a prime. Their extensions have a one-to-one correspondence with their intermediates according to the fundamental theorem of Galois theory. A division algebra is one of these without multiplicative commutativity, and can be defined as a ring with multiplicative identity, inverse, and commutativity. For 10 points, name these algebriac structures that include the rationals and reals.
Output (English): Science