Constructing Endomorphism Rings of Large Finite Global Dimension
Commutative Algebra
2020-06-03 v2 Algebraic Geometry
Category Theory
Abstract
In this paper we study endomorphism rings of finite global dimension over a ring associated to a numerical semigroup. We construct these endomorphism rings in two ways, called the lazy and greedy construction. The first main result of this paper shows that the lazy construction enables us to obtain endomorphism rings of arbitrarily large global dimension. The second main result of this paper shows that the greedy construction gives us endomorphism rings which always have global dimension two. As a consequence, for a fixed numerical semigroup, the difference of the maximal possible value and the minimal possible value of the global dimension of an endomorphism ring over that numerical semigroup can be arbitrarily large.
Keywords
Cite
@article{arxiv.1808.01704,
title = {Constructing Endomorphism Rings of Large Finite Global Dimension},
author = {Ali Mousavidehshikh},
journal= {arXiv preprint arXiv:1808.01704},
year = {2020}
}