Open AccessLong exact sequence of U-extension modules
Author(s) -
Yudi Mahatma,
Ibnu Hadi,
Bagus Sumargo
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1869/1/012139
Subject(s) - exact sequence , homomorphism , sequence (biology) , extension (predicate logic) , mathematics , integer (computer science) , combinatorics , unit (ring theory) , discrete mathematics , algebra over a field , pure mathematics , computer science , programming language , chemistry , biochemistry , mathematics education
Let R be commutative algebra with unit element. Given any R -modules M and N , and any nonzero submodule U of M , Mahatma and Muchtadi-Alamsyah defined the k -th U -extension module of N by M for every positive integer k . Further, Mahatma showed that given any short exact sequence of R -modules and R -module homomorphisms, there exists an exact sequence of U -extension modules of N by M . It is just that the sequence consists of only limited number of nonzero modules. In this paper we investigate the conditions needed by the sequence so that it can be extended into a longer one.