## Homology, Homotopy and Applications

### On constructing resolutions over the polynomial

#### Abstract

Let $k$ be a field, and $A$ be a polynomial algebra over $k$. Let $I\subseteq A$ be an ideal. We present a novel method for computing resolutions of $A/I$ over $A$. The method is a synthesis of Gröbner basis techniques and homological perturbation theory. The examples in this paper were computed using computer algebra.

#### Article information

Source
Homology Homotopy Appl. Volume 4, Number 2 (2002), 315-336.

Dates
First available in Project Euclid: 13 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.hha/1139852468

Mathematical Reviews number (MathSciNet)
MR1918515

Zentralblatt MATH identifier
0998.13012

Subjects
Primary: 13D02: Syzygies, resolutions, complexes

#### Citation

Johansson, Leif; Lambe, Larry; Sköldberg, Emil. On constructing resolutions over the polynomial. Homology Homotopy Appl. 4 (2002), no. 2, 315--336. https://projecteuclid.org/euclid.hha/1139852468.