Abstract
In this chapter, we introduce some of the key concepts from commutative algebra. Our focus will be on the concepts of rings, ideals and modules, as they are going to play a very important role in the development of the algebraic algorithms of the later chapters. In particular, we develop the ideas leading to the definition of a basis of an ideal, a proof of Hilbert’s basis theorem, and the definition of a Gröbner basis of an ideal in a polynomial ring. Another important concept, to be developed, is that of a syzygy of a finitely generated module.
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© 1993 Springer-Verlag New York, Inc.
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Mishra, B. (1993). Algebraic Preliminaries. In: Algorithmic Algebra. Texts and Monographs in Computer Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4344-1_2
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DOI: https://doi.org/10.1007/978-1-4612-4344-1_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8742-1
Online ISBN: 978-1-4612-4344-1
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