Associating fraction in subring of finite non-associative ring is at least as much as in whole ring
Suppose is a finite Non-associative ring (?) (i.e., is a not necessarily associative ring whose underlying set is finite). Suppose is a subring of . Then, the associating fraction of is at least as much as that of .
In symbols, if and , then:
In fact, the result also holds if is simply an additive subgroup of and not a subring.
The proof follows from facts (1) and (2).