The story
"Ring sum" refers to a XOR-sum of monomials, where XOR is the additive operator of a Boolean ring.
Etymology from Wiktionary, CC BY-SA 4.0.
ring sum normal form
Today it means: The form of a Boolean formula expressed using only the operators and constants of a Boolean ring (XOR, AND, 0, 1), some variables and possibly also coefficients, and without using any parentheses. Full definition →