Groups and Fields: The Two Fundamental Notions of Algebra

James B. Carrell ()
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James B. Carrell: University of British Columbia, Department of Mathematics

Chapter Chapter 2 in Groups, Matrices, and Vector Spaces, 2017, pp 11-55 from Springer

Abstract: Abstract Algebra is the mathematical discipline that arose from the problem of solving equations. If one starts with the integers $${\mathbb Z}$$ , one knows that every equation $$a+x=b$$ , where a and b are integers, has a unique solution. However, the equation $$ax=b$$ does not necessarily have a solution in $${\mathbb Z}$$ , or it might have infinitely many solutions (take $$a=b=0$$ ).

Date: 2017
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DOI: 10.1007/978-0-387-79428-0_2

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