Maximum order-index of matrices over commutative inclines: an answer to an open problem |
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| Authors: | Song-Chol Han Hong-Xing Li |
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| Institution: | a Department of Mathematics and Mechanics, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea
b School of Mathematical Sciences, Beijing Normal University, Beijing 100875, PR China |
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| Abstract: | 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 Mn(L)”, proposed by Cao, Kim and Roush in a monograph Incline Algebra and Applications, 1984, where Mn(L) is the set of all n × n matrices over an incline L. |
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| Keywords: | 16Y60 15A99 |
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