mathematical ternary operator: prime-generating function

The a-th prime according to ordering rules b in ring c; contextless default for c is the standard/typical ring of integers (Z,+,*); contextless default for b is the standard typical ordering of the ring, which is the 'normal' absolute value (signless difference/distance with/from 0) for the standard ring (Z,+,*); thus, it will usually operate as an unary operator. The function must be defined over the set of strictly positive integers in/for the first operand; generalizations may be possible. Ignores units and 0. It begins counting at 1 [in/for the first operand]; under contextless default conditions, the outputs increase strictly monotonically with respect to increase in the first input [a], starting with the least prime in (Z,+,*), namely 2. Usually denoted "p_i" or "Prime" in the literature.