Abstract
A new upper bound on the global dimension of a pullback ring is given, and Scrivanti's upper bound on the weak dimension of a pullback ring is generalized to the noncommutative case. Bibliography: 8 titles.
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REFERENCES
H. Cartan and S. Eilenberg, Homological Algebra, Princeton University Press, Princeton (1956).
J. Milnor, Introduction to Algebraic K-Theory, Princeton University Press, Princeton (1971).
A. N. Wiseman, “Projective modules over pullback rings," Math. Proc. Cambridge Phil. Soc., 97, 399–406 (1985).
A. Facchini and P. Vámos, “Injective modules over pullbacks," J. London Math. Soc., 31, 425–438 (1985).
E. Kirkman and J. Kuzmanovich, “On the global dimension of fibre products," Pacific J. Math., 134, 121–132 (1988).
S. Scrivanti, “Homological dimension of pullbacks," Math. Scand., 71, 5–15 (1992).
K. M. Cowley, “One-sided bounds and the vanishing of Ext," J. Algebra, 190, 361–371 (1997).
N. V. Kosmatov, “An upper bound for the global dimension of pullback rings," Fund. Prikl. Mat., 5, 1251–1253 (1999).
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Kosmatov, N.V. Bounds for the Homological Dimensions of Pullbacks. Journal of Mathematical Sciences 112, 4367–4370 (2002). https://doi.org/10.1023/A:1020351104689
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DOI: https://doi.org/10.1023/A:1020351104689