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Polynomial functors

Published online by Cambridge University Press:  24 October 2008

I. B. S. Passi
I. B. S. Passi
Affiliation:
Department of Mathematics, Kurukshetra University, Kurukshetra (India)
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Extract

1. Introduction: If G is a group, Z(G) its integral group-ring and AG the augmentation ideal, then we can form the Abelian groups

In (5) we have studied the structure of these Abelian groups which we called polynomial grouups. If C denotes the category of Abelian groups, then Pn and Qn are functors from C into C. We call these functors polynomial functors. The object of this work is to study the nature of these funtors. Except for n = 1, these functors are non-additive. In fact, in the sense of Eilenberg–Maclane (4) these are functors of degree exactly n (Theorem 2·3). Because of their non-additive nature, their derived functors cannot be calculated in the traditional Cartan–Eilenberg(1) method. We have to make use of the more recent theory of Dold–Puppe (3).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 3 , November 1969 , pp. 505 - 512
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Cartan, H. and Eilenberg, S.Homological algebra (Princeton, 1956).Google Scholar
(2)Dold, A.Homology of symmetric products and other functors of complexes. Ann. of Math. 68 (1958), 54–80.CrossRefGoogle Scholar
(3)Dold, A. and Puppe, D.Homologie nicht-additiver Functoren; Anwendungen, Ann. Inst. Fourier (Grenoble). 11 (1961), 201–312.CrossRefGoogle Scholar
(4)Eilenberg, S. and Maclane, S.On the groups H(π, n) II. Ann. of Math. 60 (1954), 49–139.CrossRefGoogle Scholar
(5)Passi, I. B. S.Polynomial maps on groups. J. Algebra 9 (1968), 121–151.CrossRefGoogle Scholar