Year: 2024
Type: preprint
Abstract: We present a procedure that constructs, in a combinatorial manner, a chain complex of free modules over a polynomial ring in finitely many variables, modulo an ideal generated by quadratic monomials. Applying this procedure to two specific rings and one family of rings, we demonstrate that the resulting chain complex is indeed an exact chain complex and thus a free resolution. Utilizing this free resolution, we show that, for these rings, the injective dimension is infinite, as modules over itself. Finally, we propose the conjecture that this procedure always yields a free resolution.
Source: arXiv (Cornell University)
Author: Bravo, Daniel
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4402704385