:: deftheorem Def17 defines Homomorphism MOD_4:def 17 :
for K, L being Ring
for J being Function of K,L
for V being LeftMod of K
for W being LeftMod of L
for b₆ being Function of V,W holds
( b₆ is Homomorphism of J,V,W iff ( ( for x, y being Vector of V holds b₆ . (x + y) = (b₆ . x) + (b₆ . y) ) & ( for a being Scalar of K
for x being Vector of V holds b₆ . (a * x) = (J . a) * (b₆ . x) ) ) );