Kristen A. Beck

activity

20112016

collaborators

8 papers

math.NT2016

Fixed Points of Augmented Generalized Happy Functions

Breeanne Baker Swart, Kristen A. Beck, Susan Crook +4

An augmented generalized happy function $S_{[c, b]}$ maps a positive integer to the sum of the squares of its base $b$ digits plus $c$ . In this paper, we study various properties of…

math.NT2014

Augmented generalized happy functions

Breeanne Baker Swart, Kristen A. Beck, Susan Crook +4

An augmented happy function, $S_{[c, b]}$ maps a positive integer to the sum of the squares of its base- $b$ digits and a non-negative integer $c$ . A positive integer $u$ is in a cyc…

math.AC2013

A somewhat gentle introduction to differential graded commutative algebra

Kristen A. Beck, Sean Sather-Wagstaff

Differential graded (DG) commutative algebra provides powerful techniques for proving theorems about modules over commutative rings. These notes are a somewhat colloquial introduct…

math.AC2012

Eventually linear partially complete resolutions over a local ring with $m^{4} = 0$

Kristen A. Beck

We classify the Hilbert polynomial of a local ring $(R, m)$ satisfying $m^{4} = 0$ which admits an eventually linear doubly-infinite resolution $C$ which is 'partially' complete --- tha…

math.AC2012

Krull Dimension for Differential Graded Algebras

Kristen A. Beck, Sean Sather-Wagstaff

We introduce a naive notion of a system of parameters for a homologically finite complex over a commutative noetherian local ring, and compare it to the system of parameters define…

math.AC2011

Asymptotic behavior of dimensions of syzygies

Kristen A. Beck, Micah J. Leamer

Let R be a commutative noetherian local ring, and M a finitely generated R-module of infinite projective dimension. It is well-known that the depths of the syzygy modules of M even…