草原 (meadow)
common meadow
Meadows as a New Theme in the Theory of Rings and Fields | meadow, field, division-by-zero, equational axiomatization, totalized field, rational number, real number, complex number, fraction, data linkage dynamics, tuplix calculus, process calculus, probabilistic thread algebra, Kolmogorov's probability axioms 公理$ -(-x)=xを追加する
$ Mを臺集合とし、組$ (M,+_{:M\times M\to M},\cdot_{:M\times M\to M},-_{:M\to M},{~^{-1}}_{:M\to M},0_{\in M},1_{\in M},a_{\in M})は以下を滿たすならば草原 (meadow)と呼ぶ 乘法の逆數$ ~^{-1}の性質
$ x\cdot x^{-1}=1+0\cdot x^{-1}.
反乘法律$ (x\cdot y)^{-1}=x^{-1}\cdot y^{-1} $ (1+0\cdot x)^{-1}=1+0\cdot x.
吸收元 (absorbing element)$ aの性質
$ 0^{-1}=a.
$ x+a=a.