Maximum order-index of matrices over commutative inclines: an answer to an open problem

This paper proves that the maximum order-index of n × n matrices over an arbitrary commutative incline equals ( n − 1) 2 + 1. This is an answer to an open problem “Compute the maximum order-index of a member of M n ( L)”, proposed by Cao, Kim and Roush in a monograph Incline Algebra and Applications...

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Bibliographic Details
Published in:Linear algebra and its applications 2007, Vol.420 (1), p.228-234
Main Authors: Han, Song-Chol, Li, Hong-Xing
Format: Article
Language:English
Subjects:
Algebra
Cycle
Exact sciences and technology
Incline
Incline matrix
Linear and multilinear algebra, matrix theory
Mathematics
Order-index
Reduction
Sciences and techniques of general use
Semiring
Walk
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Summary:This paper proves that the maximum order-index of n × n matrices over an arbitrary commutative incline equals ( n − 1) 2 + 1. This is an answer to an open problem “Compute the maximum order-index of a member of M n ( L)”, proposed by Cao, Kim and Roush in a monograph Incline Algebra and Applications, 1984, where M n ( L) is the set of all n × n matrices over an incline L.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2006.02.044