NONBIJECTIVE IDEMPOTENTS PRESERVERS OVER SEMIRINGS

NONBIJECTIVE IDEMPOTENTS PRESERVERS OVER SEMIRINGS

We classify linear maps which preserve idempotents on $n{\times}n$ matrices over some classes of semirings. Our results include many known semirings like the semiring of all nonnegative integers, the semiring of all nonnegative reals, any unital commutative ring, which is zero divisor free and of characteristic not two (not necessarily a principal ideal domain), and the ring of integers modulo m, where m is a product of distinct odd primes.

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