ABSTRACT
If S and T are subsets of N, then we write ST = {st | s ∈ S and t ∈ T}. For any natural number n, we write Sn = S × S × … × S (n times).
Proposition 4.1.2 (Proposition 2.57 of Pilz, 1983)
Let N be a near ring. Then
(i) For subsets R, S, T of N, (RS)T = R(ST). (ii) If h: N → N-is a homomorphism, then for all subsets S, T of N, h(ST) =
h(S) h(T), and for all subsets S-, T-of N-, h−1(ST-) ⊇ h−1(S)h−1(T). (iii) For all ideals I of N, and for all subsets S, T of N, (S + I) (T + I) = ST + I.
