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

Author

Listed:
  • Bassirou Dembele
  • Mohamed Ben Faraj Ben Maaouia
  • Mamadou Sanghare

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,-).

Suggested Citation

  • Bassirou Dembele & Mohamed Ben Faraj Ben Maaouia & Mamadou Sanghare, 2020. "Localization, Isomorphisms and Adjoint Isomorphism in the Category Comp(A - Mod)," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(4), pages 1-65, August.
    • Handle: RePEc:ibn:jmrjnl:v:12:y:2020:i:4:p:65
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    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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