Geodesic
Finite generativity of homology and cohomology modules
The Teaching of Mathematics, XXVII (2024) no. 2, p. 112

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In this paper, we consider the following question: if all homology groups of a space $X$ are finitely generated, and if $R$ is a commutative ring with identity, is it true that the homology and cohomology $R$-modules $H_i(X;R)$ and $H^i(X;R)$ are also finitely generated? We show that the answer to this question is negative in general, but affirmative if $R$ is an integral domain. In the case when $R$ is a principal ideal domain, and $H_i(X;R)$ is finitely generated for all $i$, we also discuss computing $H_i(X;M)$ and $H^i(X;M)$ for a finitely generated $R$-module $M$.
DOI : 10.57016/TM-NSXY8680
Classification : 97H99, H75
Keywords: homology, cohomology, finitely generated module. 
@article{10_57016_TM_NSXY8680,
     author = {Milica Jovanovi\'c and Petar Stoj\v{c}i\'c},
     title = {Finite generativity of homology and cohomology modules},
     journal = {The Teaching of Mathematics},
     pages = {112 },
     publisher = {mathdoc},
     volume = {XXVII},
     number = {2},
     year = {2024},
     doi = {10.57016/TM-NSXY8680},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.57016/TM-NSXY8680/}
}
TY  - JOUR
AU  - Milica Jovanović
AU  - Petar Stojčić
TI  - Finite generativity of homology and cohomology modules
JO  - The Teaching of Mathematics
PY  - 2024
SP  - 112 
VL  - XXVII
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.57016/TM-NSXY8680/
DO  - 10.57016/TM-NSXY8680
LA  - en
ID  - 10_57016_TM_NSXY8680
ER  - 
%0 Journal Article
%A Milica Jovanović
%A Petar Stojčić
%T Finite generativity of homology and cohomology modules
%J The Teaching of Mathematics
%D 2024
%P 112 
%V XXVII
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.57016/TM-NSXY8680/
%R 10.57016/TM-NSXY8680
%G en
%F 10_57016_TM_NSXY8680
Milica Jovanović; Petar Stojčić. Finite generativity of homology and cohomology modules. The Teaching of Mathematics, XXVII (2024) no. 2, p. 112 . doi: 10.57016/TM-NSXY8680

Cité par Sources :