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Register a new userA negative result on algebraic specifications of the meadow of rational numbers
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Added by
Inge Bethke
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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$mathbb{Q}_0$ - the involutive meadow of the rational numbers - is the field of the rational numbers where the multiplicative inverse operation is made total by imposing $0^{-1}=0$. In this note, we prove that $mathbb{Q}_0$ cannot be specified by the usual axioms for meadows augmented by a finite set of axioms of the form $(1+ cdots +1+x^2)cdot (1+ cdots +1 +x^2)^{-1}=1$.
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