On Decompositions of Matrices over Distributive Lattices
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-18
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Let L be a distributive lattice and Mn,q (L)(Mn(L), resp.) the semigroup (semiring, resp.) of n × q (n × n, resp.) matrices over L.
In this paper, we show that if there is a subdirect embedding from distributive lattice L to the direct product ∏i=1mLi of distributive lattices L1,L2, …,Lm, then there will be a corresponding subdirect embedding from the matrix semigroup Mn,q(L) (semiring Mn(L), resp.) to semigroup ∏i=1mMn,q(Li) (semiring ∏i=1mMn(Li), resp.).
Further, it is proved that a matrix over a distributive lattice can be decomposed into the sum of matrices over some of its special subchains.
This generalizes and extends the decomposition theorems of matrices over finite distributive lattices, chain semirings, fuzzy semirings, and so forth.
Finally, as some applications, we present a method to calculate the indices and periods of the matrices over a distributive lattice and characterize the structures of idempotent and nilpotent matrices over it.
We translate the characterizations of idempotent and nilpotent matrices over a distributive lattice into the corresponding ones of the binary Boolean cases, which also generalize the corresponding structures of idempotent and nilpotent matrices over general Boolean algebras, chain semirings, fuzzy semirings, and so forth.
American Psychological Association (APA)
Chen, Yizhi& Zhao, Xianzhong. 2014. On Decompositions of Matrices over Distributive Lattices. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-454058
Modern Language Association (MLA)
Chen, Yizhi& Zhao, Xianzhong. On Decompositions of Matrices over Distributive Lattices. Journal of Applied Mathematics No. 2014 (2014), pp.1-10.
https://search.emarefa.net/detail/BIM-454058
American Medical Association (AMA)
Chen, Yizhi& Zhao, Xianzhong. On Decompositions of Matrices over Distributive Lattices. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-454058
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-454058