Texas Project NExT Journal

Vol. 1 (2003), pp. 10-21.

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Projective resolutions from tensoring syzygies

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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