E-EXACT SEQUENCE AND SOME RESULTS

Authors : Abuzer Gündüz

Pages : 319-328

Doi:10.55071/ticaretfbd.1434248

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Publication Date : 2024-12-27

Article Type : Research Paper

Abstract :Let R be a commutative ring with identity, M be a R-module and N be a submodule of M. N is called to be essential (large) in M if N∩Rm≠0 for any nonzero element m∈M and we showed by N≤_e M. A sequence of R-modules and R-morphisms …→┴ M_(i-1) □(→┴f_(i-1) M_i →┴f_i ) M_(i+1) →┴f_(i+1) … is called exact at M_i if Im(f_(i-1) )=Ker (f_i). Also this sequence is called e-exact at M_i if Im(f_(i-1))≤_e Ker(f_i) and it is called e-exact if it is e-exact at each M_i. In this note, we present the concept of the characterization of E-homotopy and E-resolution with some results such as chain map for e-exact sequence and comparing theorem for e-exact sequence.
Keywords : E-injektif modüller, e-tam diziler, contravariant functor, homolojik cebir