Solving Problems in Scalar Algebras of Reduced Powers

Abstract

Following our previous work, we suggest here a large class of algebras of scalars in which simultaneous and correlated computations can be performed owing to the existence of surjective algebra homomorphisms. This may replace the currently used traditional computations in which only real or complex scalars are used, or occasionally, nonstandard ones. The usual real, complex, or nonstandard scalars are included in the mentioned large class of algebras. Such simultaneous and correlated computations offer a depth of insight which has so far been missed when only using the few traditional kind of scalars.