1993 | OriginalPaper | Buchkapitel
Algebraic Preliminaries
verfasst von : Bhubaneswar Mishra
Erschienen in: Algorithmic Algebra
Verlag: Springer New York
Enthalten in: Professional Book Archive
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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.