On Some Relationships Between Spectral Sequences And The New Exact Sequences

  • Dheia Gaze Salih Al-Khafajy Department of Mathematics College of Computer Science and Mathematics Al-Qadisiya University

Abstract

     In this paper I introduce and study relationships between spectral

sequences and the new exact sequences . I will show that the  new exact  sequence is the second derived exact couple .

       Let

                                              

                                  

                                          

 

be an exact couple ,  we derive  to get the second exact couple    which is the new exact sequence  . the process of derivation can

 be iterated indefinitely, yielding an infinite sequence of exact couples .

      I establish some results ,for examples ; 

      The class of all exact couples and morphisms between these couples formed a category . There is a functor from the category of   into   .

     If   

 .

       If    be any   , then

 , and    .

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Published
2017-09-16
How to Cite
Gaze Salih Al-Khafajy, D. (2017). On Some Relationships Between Spectral Sequences And The New Exact Sequences. Journal of Al-Qadisiyah for Computer Science and Mathematics, 3(1), 59-70. Retrieved from https://qu.edu.iq/journalcm/index.php/journalcm/article/view/240
Section
Math Articles