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Baer-invariants and extensions relative to a variety

Published online by Cambridge University Press:  24 October 2008

Abraham S.-T. Lue
Abraham S.-T. Lue
Affiliation:
King's College, London
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Extract

This paper examines the relationship between extensions in a variety and general extensions in the category of associative algebras. Our associative algebras are all unitary, over some fixed commutative ring Λ with identity, but while our discussion will be restricted to this category, it is clear that obvious analogues exist for groups, Lie algebras and Jordan algebras. (We use the notion of a bimultiplication of an associative algebra. In (2), Knopfmacher gives the definition of a bimultiplication in any variety of linear algebras.)

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 3 , July 1967 , pp. 569 - 578
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Fröhlich, A.Baer-invariants of algebras. Trans. Amer. Math. Soc. 109 (1963), 221–244.CrossRefGoogle Scholar
(2)Knopfmacher, J.Extensions in varieties of groups and algebras. Acta Math. 115 (1966), 17–50.CrossRefGoogle Scholar
(3)Lue, A. S.-T. Non-Abelian cohomology of associative algebras (to appear).Google Scholar
(4)MacLane, S.Extensions and obstructions for rings. Illinois J. Math. 2 (1958), 316–345.Google Scholar