Open AccessTHE FIRST U-EXTENSION MODULE AS CLASSES OF SHORT U-EXACT SEQUENCES
Author(s) -
Yudi Mahatma
Publication year - 2021
Publication title -
jurnal matematika unand/jurnal matematika unand
Language(s) - English
Resource type - Journals
eISSN - 2721-9410
pISSN - 2303-291X
DOI - 10.25077/jmu.10.4.553-560.2021
Subject(s) - extension (predicate logic) , exact sequence , sequence (biology) , mathematics , resolution (logic) , construct (python library) , equivalence (formal languages) , set (abstract data type) , equivalence relation , projective test , discrete mathematics , pure mathematics , algebra over a field , computer science , programming language , biology , genetics
Inspired by the notions of the U-exact sequence introduced by Davvaz and Parnian-Garamaleky in 1999, and of the chain U-complex introduced by Davvaz and Shabani-Solt in 2002, Mahatma and Muchtadi-Alamsyah in 2017 developed the concept of the U-projective resolution and the U-extension module, which are the generalizations of the concept of the projective resolution and the concept of extension module, respectively. It is already known that every element of a first extension module can be identified as a short exact sequence. To the simple, there is a relation between the first extension module and the short exact sequence. It is proper to expect the relation to be provided in the U-version. In this paper, we aim to construct a one-one correspondence between the first U-extension module and the set consisting of equivalence classes of short U-exact sequence.Keywords: Chain U-complex, U-projective resolution, U-extension module