Homework Statement
Let (R,+, ·) be an algebraic object that satisfies all the axioms for a ring
except for the multiplicative identity. Define addition and multiplication in
R × Z by
(a, n) + (b,m) = (a + b, n + m) and
(a, n) · (b,m) = (ab + ma + nb, nm).
Show that (R × Z,+, ·) is a...