Summary: This paper proves that if an additively idempotent semiring is inherently nonfinitely based, so is its multiplicative reduct. As an application, we show that every finite additively idempotent semiring whose cardinality is less than seven or satisfying \({x^n} \approx x\) is not inherently nonfinitely based. Also, we show that the class of all locally finite members of the additively idempotent semiring variety defined by \({x^n} \approx x\) forms a variety. Finally, we provide a simple proof for the main result of correlative literature.