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On the existence of freely generated algebras

Published online by Cambridge University Press:  24 October 2008

H. F. J. Lowig
H. F. J. Lowig
Affiliation:
Department of MathematicsUniversity of Tasmania
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Extract

Throughout this paper, the concept of a ‘freely generated algebra’ will be meant in the sense of (3), Definition 2·1. It is understood that all conventions concerning terminology and notation introduced in (3) hold in this paper. In particular, it is understood that the sign denotes a freely generated algebra, and that the definition-set and the free basis of are denoted by C and D respectively. The letter q will denote a cardinal number.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 4 , October 1957 , pp. 790 - 795
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

REFERENCES

(1)Birkhoff, G.On the structure of abstract algebras. Proc. Camb. Phil. Soc. 31 (1935), 433–54.CrossRefGoogle Scholar
(2)Landau, E.Grundlagen der Analysis (Leipzig, 1930).Google Scholar
(3)Löwig, H. F. J.On the properties of freely generated algebras. J. reine angew. Math. 190 (1952), 65–74.CrossRefGoogle Scholar