I am reading Stephen Lovett's book, "Abstract Algebra: Structures and Applications" and am currently focused on Section 6.2: Rings of Fractions ...(adsbygoogle = window.adsbygoogle || []).push({});

I need some help with some remarks following Definition 6.2.4 ... ... ...

The remarks following Definition 6.2.4 reads as follows:

In the above text from Lovett we read the following:

" ... ... it is not hard to show that if we had taken ##D = { \mathbb{Z} }^{ \gt 0 }## we would get a ring of fractions that is that is isomorphic to ## \mathbb{Q}##. ... ... "

Can someone please help me to understand this statement ... how is such an isomorphism possible ... in particular, how does one achieve a one-to-one and onto homomorphism from the positive integers to the negative elements of ##\mathbb{Q}## as well as the positive elements ...

Hope someone can help ... ...

Peter

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To enable readers to understand Lovett's approach to the rings of fraction construction, I am providing Lovett Section 6.2 up to an including the remarks following Definition 6.2.4 ... as follows:

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# I Rings of Fractions ... Lovett, Section 6.2 ...

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