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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.
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참고문헌 (13)
참고문헌 신청
C.-G. Cao / 2005 / Linear preservers between matrix modules over connected commutative rings / Linear Algebra Appl. 397 : 355 ~ 366
D. Dolˇzan / 2009 / Idempotent matrices over antirings / Linear Multilinear Algebra Appl. 431 (5) : 823 ~ 832
G.-H. Chan / 1987 / Linear preservers on matrices / Linear Algebra Appl. 93 : 67 ~ 80
J. S. Golan / 1992 / The theory of semirings with applications in mathematics and theoretical computer science, Pitman Monographs and Surveys in Pure and Applied Mathematics, 54 / Longma
J.-T. Chan / 2006 / Mappings on matrices: invariance of functional values of matrix products / J. Aust. Math. Soc. 81 (2) : 165 ~ 184
D. Dolˇzan / 2009 / Idempotent matrices over antirings / Linear Multilinear Algebra Appl. 431 (5) : 823 ~ 832
G.-H. Chan / 1987 / Linear preservers on matrices / Linear Algebra Appl. 93 : 67 ~ 80
J. S. Golan / 1992 / The theory of semirings with applications in mathematics and theoretical computer science, Pitman Monographs and Surveys in Pure and Applied Mathematics, 54 / Longma
J.-T. Chan / 2006 / Mappings on matrices: invariance of functional values of matrix products / J. Aust. Math. Soc. 81 (2) : 165 ~ 184
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