Abstract
In this chapter, we develop the basic tools for working with monomial ideals. Section 1.1 introduces the main players. Motivated by some properties from this section, Section 1.2 contains a brief discussion of integral domains. Section 1.3 deals with some aspects of generating sets for monomial ideals. The optional Section 1.4 on noetherian rings is a natural follow-up. The chapter concludes with explorations of some numerical aspects of monomials and monomial ideals in Sections 1.5 and 1.6. The parallel Macaulay2 material here explores these notions computationally and lays the groundwork for more elaborate programming down the road.
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See the Concluding Notes of Appendix A for more about this.
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Moore, W.F., Rogers, M., Sather-Wagstaff, S. (2018). Fundamental Properties of Monomial Ideals. In: Monomial Ideals and Their Decompositions. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-96876-6_1
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DOI: https://doi.org/10.1007/978-3-319-96876-6_1
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