Linear Algebra pp 167-185 | Cite as

# Gradations and homology

Chapter

## Abstract

Let is given and that to every subspace .

*E*be a vector space and*G*be an abelian group. Suppose that a direct decomposition$$E = \sum\nolimits_{\alpha \in I} {{E_\alpha }} $$

(6.1)

*E*_{ α }an element*k*(α) of*G*is assigned such that the mapping*a→k((x)*is injective. Then*E*is called a*G-graded vector space. G*is called the*group of degrees*for*E*. The vectors of*E*_{ α }are called*homogeneous of degree k*(*α*) and we shall write$$\deg x = k(\alpha ),x \in {E_\alpha }$$

## Keywords

Degree Zero Homogeneous Element Linear Isomorphism Differential Algebra Grade Vector Space
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## Copyright information

© Springer-Verlag New York Inc. 1975