Мнемочисла и мнемовекторы. I

Abstract

To study the rings of mnemonumbers we introduce the mnemofication functor from the category of normed spaces over non-trivially normed field into the category of ultra-metric Banach modules over ring of mnemonumbers. We found a complete non-trivially normed subfield in the ring of mnemonumbers isomorphic to the field of formal power series with coefficient in the basic field, so the ring of mnemonumbers is Banach algebra over it and corresponding modules are Banach spaces.