Abstract
In this chapter we describe a number of axioms for sets on which addition and multiplication are defined. These axioms were originally found by isolating the basic properties of addition and multiplication which are common to all or most of the examples we already know: ℤ, ℚ, ℝ, ℂ. A ring, a commutative ring, or a field will be defined as a set with addition and multiplication satisfying certain of the axioms.
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© 1979 Springer-Verlag New York Inc.
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Childs, L. (1979). Rings and Fields. In: A Concrete Introduction to Higher Algebra. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0065-6_8
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DOI: https://doi.org/10.1007/978-1-4684-0065-6_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-0067-0
Online ISBN: 978-1-4684-0065-6
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