The authors study ring-like domains, i.e. zero-symmetric Abelian right near-rings. Considering for near-rings the left and right orders defined for rings by D. Tamari in 1948 [Bull. Am. Math. Soc. 54, 153-158 (1948; Zbl 0032.00601)], they show that the left order of such a near-ring can be 0, 1 or infinite, while the right order can be arbitrary. Some of the results are: 1. A near-ring with unity has both orders greater or equal to 1. 2. There exist near-rings, which are not rings, of type \((1,k)\) or \((0,k)\), for all positive integers \(k\). 3. The centralizer near-ring of the group \((\mathbb{Z},+)\) with respect to \(A=\{\text{id},-\text{id}\}\) is of type infinite on the left and on the right.
For the entire collection see [Zbl 0998.00012].