Localization, Isomorphisms and Adjoint Isomorphism in the Category Comp(A - Mod)

Bassirou Dembele, Mohamed Ben Faraj Ben Maaouia and Mamadou Sanghare

Journal of Mathematics Research, 2020, vol. 12, issue 4, 65

Abstract: A and B are considered to be non necessarily commutative rings and X a complex of (A - B) bimodules. The aim of this paper is to show that- The functors \overline{EXT}^n_{Comp(A-Mod)}(X,-)- Comp(A-Mod) \longrightarrow Comp(B-Mod) and Tor_n^{Comp(B-Mod)}(X,-)- Comp(B-Mod) \longrightarrow Comp(A-Mod) are adjoint functors. The functor S_C^{-1}() commute with the functors X\bigotimes - , Hom^{\bullet}(X,-) and their corresponding derived functors \overline{EXT}^n_{Comp(A-Mod)}(X,-) and Tor_n^{Comp(B-Mod)}(X,-).

Date: 2020
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