Texas Project NExT Journal
Vol. 1 (2003), pp. 10-21.

Projective resolutions from tensoring syzygies

Nathan Smith

MSC (2000): 13D02

Key words: Homological methods Syzygies, resolutions, complexes

Abstract: We introduce a method of obtaining a projective bimodule resolution for a quotient $\Lambda$ of a path algebra by repeatedly tensoring a canonical short exact sequence with $\Omega^1_{\Lambda^e}(\Lambda)$. In one form our method gives a normalized bar resolution, and we discuss how to modify our construction to obtain a computationally more tractable resolution. We then give a method of computing resolutions of right $\Lambda$-modules given in the form of a presentation.

University of Texas at Tyler, Tyler, TX 75799
e-mail: nathan@math.uttyl.edu

Received by Editor: June 14, 2002 and, in revised form April 18, 2003.
Posted: June 9, 2003.

Copyright 2003