Plus and times
Richard Arnold, Anthony P. Morse · Pacific Journal of Mathematics · 1976
Postulated here are very general but nevertheless concrete notions of plus and times.The generality achieved lessens the need for abstract linear spaces.The addition and multiplication are universally associative and commutative and multiplication rather widely distributes over addition.The addable entities are of three general types: numbers, functions, and classes.The numbers are the finite complex numbers along with certain infinities.The addable functions are addable valued nonvacuous functions.The addable classes are free of numbers and ordered pairs; they are structured nonvacuous classes of addable entities.Many addable classes arise, as in §5, as congruence classes from an equivalence relation.In particular, the usual complex Lebesgue classes are among the addable classes.