Homomorphism theories for universal algebras
Hans‐Jürgen Hoehnke · Proceedings of the Edinburgh Mathematical Society · 1968
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.