RT info:eu-repo/semantics/bookPart
T1 Binomial Ideals and Congruences on Nn
A1 Matusevich, Laura Felicia
A1 Ojeda, Ignacio
K1 Binomial ideals
K1 Ideales binomiales
K1 Graded algebras
K1 Álgebra graduada
K1 Congruences
K1 Congruencias
AB A congruence on Nn is an equivalence relation on Nn that is compatible with the additive structure. If k is a field, and I is a binomial ideal in k[X1,…,Xn] (that is, an ideal generated by polynomials with at most two terms), then I induces a congruence on Nn by declaring u and v to be equivalent if there is a linear combination with nonzero coefficients of Xu and Xv that belongs to I. While every congruence on Nn arises this way, this is not a one-to-one correspondence, as many binomial ideals may induce the same congruence. Nevertheless, the link between a binomial ideal and its corresponding congruence is strong, and one may think of congruences as the underlying combinatorial structures of binomial ideals. In the current literature, the theories of binomial ideals and congruences on Nn are developed separately. The aim of this survey paper is to provide a detailed parallel exposition, that provides algebraic intuition for the combinatorial analysis of congruences. For the elaboration of this survey paper, we followed mainly (Kahle and Miller Algebra Number Theory 8(6):1297–1364, 2014) with an eye on Eisenbud and Sturmfels (Duke Math J 84(1):1–45, 1996) and Ojeda and Piedra Sánchez (J Symbolic Comput 30(4):383–400, 2000).
PB Springer
SN 978-3-319-96827-8
YR 2018
FD 2018
LK http://uvadoc.uva.es/handle/10324/40808
UL http://uvadoc.uva.es/handle/10324/40808
LA eng
NO Greuel, Gert-Martin; Narváez Macarro, Luis; Xambó-Descamps, Sebastià (coords.). Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics: Festschrift for Antonio Campillo on the Occasion of his 65th Birthday. Springer, 2018, p. 429-454
NO Producción Científica
DS UVaDOC
RD 25-sep-2020