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Let's $(\mathbb{C},\mathbb{C})$ be a ordered paired of elements form $\mathbb{C}$ when $\mathbb{C}$ is defined as (a,b).
addition and multiplication is defined as in $\mathbb{C}$.
How do I prove it is not a field if $\mathbb{C}$ is a field

rschwieb
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gbox
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    $(a,b)$ denotes AN ordered pair. The set of ordered pairs is usually denoted by $A\times B$. In this case $\Bbb{C\times C}$ is not a field, rather than just $(\Bbb{C,C})$. – Asaf Karagila Nov 17 '14 at 10:53

1 Answers1

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$(2,0)*(0,2)=(0,0)$. Therefore it has zero-divisors. (2,0) does not have an inverse element. ...

Loreno Heer
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