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NONBIJECTIVE IDEMPOTENTS PRESERVERS OVER SEMIRINGS
Marko Orel 대한수학회 2010 대한수학회지 Vol.47 No.4
We classify linear maps which preserve idempotents on n×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.
NONBIJECTIVE IDEMPOTENTS PRESERVERS OVER SEMIRINGS
Orel, Marko Korean Mathematical Society 2010 대한수학회지 Vol.47 No.4
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.