Abstract
We study additive functions given on a category of finitely generated projective modules. Using these functions, we define p-minimal epimorphisms and give a necessary and sufficient condition for their existence. We prove results concerning the structure of p-minimal chains of projective modules.
Similar content being viewed by others
REFERENCES
P. M. Cohn, "Some remarks on the invariant basis property," Topology, 5, 215–228 (1966).
J. R. Stallings, "A finitely presented group whose 3-dimensional integral homology is not finitely generated," Amer. J. Math., 85, 541–543 (1963).
V. A. Artamonov, "Projective nonfree modules over group rings of solvable groups," Mat. Sb., 116, 232–244 (1981).
M. Dunwoody, "Relation modules," Bull. London Math. Soc., 4, 151–155 (1972).
J. Lewin, "Projective modules over group-algebras of torsion-free groups," Mich. Math. J., 29, 59–65 (1982).
E. Dyer and A. T. Vasquez, "An invariant for finitely generated projectives over Z| G|," Pure Appl. Algebra, 7, 241–248 (1976).
H. Bass, "Euler characteristics and characters of discrete groups," Invent. Math., 35, 155–196 (1976).
K. S. Brown, Cohomology of Groups, Springer, New York (1982).
W. Cockroft and R. Swan, "On homotopy type of certain two-dimensional complexes," Proc. London Math. Soc., 11, 193–202 (1961).
V. V. Sharko, Functions on Manifolds[in Russian], Naukova Dumka, Kiev (1990).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sharko, V.V. Additive Functions and Chain Complexes of Projective Modules. Ukrainian Mathematical Journal 56, 296–304 (2004). https://doi.org/10.1023/B:UKMA.0000036103.30114.bd
Issue Date:
DOI: https://doi.org/10.1023/B:UKMA.0000036103.30114.bd