Abstract
This chapter contains a review of certain fundamental concepts in abstract algebra for use throughout the text. Section A.1 deals with the basic properties of commutative rings with identity, Section A.2 focuses on polynomial rings, and Section A.3 introduces ideals. As we discuss in the introduction to this text, these objects occur in numerous areas of mathematics. We strongly encourage readers to make sure they are familiar with the material on generators of ideals in Section A.3, as this notion is absolutely fundamental for this text.
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Notes
- 1.
This is a consequence of “quadratic reciprocity”.
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Moore, W.F., Rogers, M., Sather-Wagstaff, S. (2018). Appendix A: Foundational Concepts. In: Monomial Ideals and Their Decompositions. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-96876-6_8
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DOI: https://doi.org/10.1007/978-3-319-96876-6_8
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