# Realization of long exact sequences of abelian groups.

Publicacions Matemàtiques (1990)

- Volume: 34, Issue: 1, page 67-76
- ISSN: 0214-1493

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topPressman, Irwin S.. "Realization of long exact sequences of abelian groups.." Publicacions Matemàtiques 34.1 (1990): 67-76. <http://eudml.org/doc/41114>.

@article{Pressman1990,

abstract = {Given a long exact sequence of abelian groupsL: ... → Li-1 →ξi-1 Li →ξi Li+1 → ...a short exact sequence of complexes of free abelian groups is constructed whose cohomology long exact sequence is precisely L. In this sense, L is realized. Two techniques which are introduced to reduce or replace lengthy diagram chasing arguments may be of interest to some readers. One is an arithmetic of bicartesian squares; the other is the use of the fact that categories of morphisms of abelian categories are themselves abelian.},

author = {Pressman, Irwin S.},

journal = {Publicacions Matemàtiques},

keywords = {Teoría de grupos; Grupos; Grupos abelianos; category of abelian groups; cohomology of complexes; cohomology sequence of a short exact sequence of complexes of abelian groups; long exact sequence of abelian groups; bicartesian squares},

language = {eng},

number = {1},

pages = {67-76},

title = {Realization of long exact sequences of abelian groups.},

url = {http://eudml.org/doc/41114},

volume = {34},

year = {1990},

}

TY - JOUR

AU - Pressman, Irwin S.

TI - Realization of long exact sequences of abelian groups.

JO - Publicacions Matemàtiques

PY - 1990

VL - 34

IS - 1

SP - 67

EP - 76

AB - Given a long exact sequence of abelian groupsL: ... → Li-1 →ξi-1 Li →ξi Li+1 → ...a short exact sequence of complexes of free abelian groups is constructed whose cohomology long exact sequence is precisely L. In this sense, L is realized. Two techniques which are introduced to reduce or replace lengthy diagram chasing arguments may be of interest to some readers. One is an arithmetic of bicartesian squares; the other is the use of the fact that categories of morphisms of abelian categories are themselves abelian.

LA - eng

KW - Teoría de grupos; Grupos; Grupos abelianos; category of abelian groups; cohomology of complexes; cohomology sequence of a short exact sequence of complexes of abelian groups; long exact sequence of abelian groups; bicartesian squares

UR - http://eudml.org/doc/41114

ER -

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