Characteristic Direct product of the Rings Let the rings, $R_i$ and its direct product, $R = \Pi_1 ^{n}R_i = R_1 \times R_2 \times ... \times R_n$
Say the $Char(R_i) = m_i$
(1) $Char(R)$ = $lcm(m_1,m_2,...m_n)$
If all the rings, $R_i$ are commutative,  The statement (1) is surely true.
But what if the There are some rings that not commutative. 
Does statement (1) is true?
(I.E. IS still $(1)$ true that regardelss of the $R_i$ is a commutative or not ?)
Thanks.

Generally, if you have two groups $G_1$ and $G_2$, then the order of an element $ (g_1, g_2) \in G_1 \times G_2$ is simply lcm(ord($g_1$), ord($g_2$)). If the order of one of the elements is infinite, we simply take the lcm to mean infinite. 
The underlying additive group of any ring is abelian. And the characteristic of a nonzero unital ring is just the order of the multiplicative identity $1$ in that abelian group. 
