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Titlebook: Rings, Fields, and Vector Spaces; An Introduction to A B. A. Sethuraman Textbook 1997 Springer-Verlag New York 1997 Abstract algebra.Micros

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Straightedge and Compass Constructions,Having covered an immense amount of abstract material in the previous six chapters, we are finally at the point where we can study constructibility!
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Introduction,1, 2, 3,.... Then, we learn about the process of “taking away,” that is, the process of subtracting one number from another, and as a consequence, we learn about the number 0 as well as the numbers −1, −2, −3,....Thus acquainted with the integers, we learn multiplication as a shortcut to addition-ad
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Divisibility in the Integers,ℤ and is very familiar to us-in fact, we were introduced to this set so early in our lives that we think of ourselves as having grown up with the integers! Moreover, we view ourselves as having completely absorbed the process of integer division; we unhesitatingly describe 3 as dividing 99 and equal
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Vector Spaces,hings one would like to do is somehow measure . is relative to D. Of course, “how big” is a loose term, and we need to make this question more precise. To do so, we need to invoke some ideas from the theory of vector spaces.
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Introduction,ding four 3s together is the same as multiplying 3 by 4. After several years of multiplication tables, we are taught fractions (usually in the context of dividing two pies among five people), and as a result, we learn about the rational numbers.
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