Yeah, in this particular text J holds the same value as \(\displaystyle \mathbb{Z}\).

I'm teaching myself abstract algebra and I'm not familiar with the notation \(\displaystyle J, 2J, 3J, ... , nJ\). Is this purely implying a scalar quantity? Such that \(\displaystyle nJ = ... -3n, -2n, -n, 0, n, 2n, 3n ...\)?