NONBIJECTIVE IDEMPOTENTS PRESERVERS OVER SEMIRINGS

Title & Authors
NONBIJECTIVE IDEMPOTENTS PRESERVERS OVER SEMIRINGS
Orel, Marko;

Abstract
We classify linear maps which preserve idempotents on $\small{n{\times}n}$ 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.
Keywords
linear preserver;semiring;idempotent matrix;
Language
English
Cited by
1.
Onn×nmatrices over a finite distributive lattice, Linear and Multilinear Algebra, 2012, 60, 2, 131
2.
On linear operators strongly preserving invariants of Boolean matrices, Czechoslovak Mathematical Journal, 2012, 62, 1, 169
3.
Idempotent matrices over antirings, Linear Algebra and its Applications, 2009, 431, 5-7, 823
4.
On Decompositions of Matrices over Distributive Lattices, Journal of Applied Mathematics, 2014, 2014, 1
5.
The Invertible Linear Operator Preserving {1,2}-Inverses of Matrices over Semirings, Pure Mathematics, 2015, 05, 01, 8
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