论文标题
基本算术的逆半群理论
The Inverse Semigroup Theory of Elementary Arithmetic
论文作者
论文摘要
我们将加法和乘法的基本算术操作进行了对N上的单调注射的基本算术操作，并描述和研究并研究了同样考虑其广义倒置的基形成型。这导致了众所周知的经典逆肌反应，以及一种新型的逆肌逆（算术逆元基a），以自然的数字理论方式将其概括为概括。 基于此，我们从算术上解释了经典的逆半群理论概念，反之亦然。 A内的组成和正常形式基于中国的余数定理，最小的生成集对应于所有主要的多环类单体。然后，这给出了Nivat＆Perot的多环子单体，混合radix计数系统以及P-ADIC规范和距离之间的正常形式。
We curry the elementary arithmetic operations of addition and multiplication to give monotone injections on N, and describe & study the inverse monoids that arise from also considering their generalised inverses. This leads to well-known classic inverse monoids, as well as a novel inverse monoid (the 'arithmetic inverse monoid' A) that generalises these in a natural number-theoretic manner. Based on this, we interpret classic inverse semigroup theoretic concepts arithmetically, and vice versa. Composition and normal forms within A are based on the Chinese remainder theorem, and a minimal generating set corresponds to all prime-order polycyclic monoids. This then gives a close connection between Nivat & Perot's normal forms for polycyclic monoids, mixed-radix counting systems, and p-adic norms & distances.
