The behavior of homological dimensions

Theory of Approximation and Applications

مقاله 1، دوره 7، شماره 1، مرداد 2013، صفحه 1-10   

نوع مقاله: Research Articles

نویسندگان

M. Ansari؛ E. Hosseini^*

Department of Mathematics, Islamic Azad University, Gachsaran branch, Gachsaran, Iran.

چکیده

Let R be a commutative noetherian ring. We study the behavior of injective
and at dimension of R-modules under the functors Hom_R(-,-) and -×_R-.

مراجع

[1] D. A. Buchsbaum, Categories and duality, Trans. Amer. Math. Soc. 80 (1955), 1-34.
[2] H. Cartan, S. Eilenberg, Homological algebra, Princeton University Press, (1956).
[3] H. B. Foxby, A homological theory of complexes of modules, Unpublished Notes,
(1981).
[4] G. Hochshild, Relative homological algebra, Trans. Amer. Math. Soc. 82 (1956),
246-269.
[5] B. Iversen, Cohomology of sheaves, Springer-Verlag, New Yourk, (1998).
[6] S. Mac Lane, Categories for the working mathematician, Springer-Verlag, New
Yourk, (1998).

[7] E. Kirkman, J. Kuzmanovich ,Algebra with larg homological dimensions, Proc.
Amer. Math. Soc. 109, (1990), 903-906.
[8] C. A.Weible, An introduction to homological algebra, Cambridge studies in advanced
mathematics 38, Cambridge, (2003).