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Rings with Inquiry (Janssen and Lindsey)

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    82145

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    In [1], the author defines a purely structural property as one that “can be defined wholly in terms of the concepts same and different, and part and whole (along with purely logical concepts).” This definition and its reference to parts and wholes calls to mind the history of the word algebra itself, which comes from the Arabic al-jabr, literally meaning “the reunion of broken parts”. One of the concepts fundamental to the historical development of algebra is the notion of factorization; closely related questions that have driven the development of algebra over the centuries are: when does a polynomial equation have solutions in a particular number system, and is there a systematic way to find them? The goal of this book is to explore the idea of factorization from an abstract perspective.

    References

    [1] J. Franklin, An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure, Palgrave Macmillan UK, 2014

    This page titled Rings with Inquiry (Janssen and Lindsey) is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Michael Janssen & Melissa Lindsey via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.