Factor rank preservers of matrices over additively-idempotent multiplicatively-cancellative semirings

Abstract

Here, we characterize the linear operators that preserve factor rank of matrices over additively-idempotent multiplicatively-cancellative semirings. The main results in this paper generalize the corresponding results on the two element Boolean algebra [L. B. Beasley and N. J. Pullman, Boolean-rank-preserving opeartors and Boolean-rank-1 spaces, Linear Algebra Appl. 59 (1984) 55–77] and on the max algebra [R. B. Bapat, S. Pati and S.-Z. Song, Rank preservers of matrices over max algebra, Linear Multilinear Algebra 48(2) (2000) 149–164]; and hold on max-plus algebra and some other tropical semirings.