Koszul Algebras Defined by Three Relations

Autor:	Adam Boocher, Srikanth B. Iyengar, S. Hamid Hassanzadeh
Rok vydání:	2017
Předmět:	Discrete mathematics Betti number Polynomial ring 010102 general mathematics Dimension (graph theory) 01 natural sciences Combinatorics 0103 physical sciences 010307 mathematical physics Koszul algebra Ideal (ring theory) 0101 mathematics Commutative property Mathematics
Zdroj:	Homological and Computational Methods in Commutative Algebra ISBN: 9783319619422
DOI:	10.1007/978-3-319-61943-9_3
Popis:	This work concerns commutative algebras of the form R = Q∕I, where Q is a standard graded polynomial ring and I is a homogenous ideal in Q. It has been proposed that when R is Koszul the ith Betti number of R over Q is at most \(\binom{g}{i}\), where g is the number of generators of I; in particular, the projective dimension of R over Q is at most g. The main result of this work settles this question, in the affirmative, when g ≤ 3.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::20142d972b92c04c4f2dc8e263ec118e https://doi.org/10.1007/978-3-319-61943-9_3 Zobrazit plný text záznamu