The zero flag is a single bit flag that is a central feature on most conventional CPU architectures (including x86, ARM, PDP-11, 68000, 6502, and numerous others).
The zero flag is typically abbreviated Z or ZF or similar in most documentation and assembly languages.
It is set to 1, or true, if an arithmetic result is zero, and reset otherwise.
This includes results which are not stored, as most traditional instruction sets implement the compare instruction as a subtract where the result is discarded.
It is also common that processors have a bitwise AND-instruction that does not store the result.