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Homomorphism theories for universal algebras

Published online by Cambridge University Press:  20 January 2009

Hans-Jürgen Hoehnke
Hans-Jürgen Hoehnke
Affiliation:
Deutsche Akademie der Wissenschaften Zu Berlin, Forschungsgemeinschaft, Institut für Reine Mathematik.
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It is well-known that a homomorphism ø(A→B) between groups A and B induces a homomorphism ø*(ZA→ZB) between the corresponding group rings ZA and ZB over the ring of integers Z. The identical congruence O on B and the unit element eB of B can be characterised by the equations x–y = 0 and x–eB = 0 (x,y ∈ B) respectively. Similarly the congruence Γø corresponding to ø and the corresponding normal subgroup of A are

and {x∈A1 = A,(x–eA)ø = 0} respectively.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 16 , Issue 1 , June 1968 , pp. 19 - 35
Copyright
Copyright © Edinburgh Mathematical Society 1968

References

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