Skip to main content
SpringerLink
Log in

Indecomposable matrices over a distributive lattice

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

In this paper, the concepts of indecomposable matrices and fully indecomposable matrices over a distributive lattice L are introduced, and some algebraic properties of them are obtained. Also, some characterizations of the set F n (L) of all n × n fully indecomposable matrices as a subsemigroup of the semigroup H n (L) of all n × n Hall matrices over the lattice L are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Frobenius: Über Matrizen aus nichtnegativen Elementen. Sitzb. d. Preuss, Akad. d. Wiss. (1912), 456–477.

  2. M. Marcus, H. Minc: Disjoint pairs of sets and incidence matrices. Illinois J. Math. 7 (1963), 137–147.

    MATH  MathSciNet  Google Scholar 

  3. Š. Schwarz: The semigroup of fully indecomposable relations and Hall relations. Czechoslovak Math. J. 23 (1973), 151–163.

    MATH  MathSciNet  Google Scholar 

  4. C. Y. Chao: On a conjecture of the semigroup of fully indecomposable relations. Czechoslovak Math. J. 27 (1977), 591–597.

    MATH  MathSciNet  Google Scholar 

  5. C. Y. Chao, M. C. Zhang: On the semigroup of fully indecomposable relations. Czechoslovak Math. J. 33 (1983), 314–319.

    MATH  MathSciNet  Google Scholar 

  6. J. Y. Shao, Q. Li: On the indices of convergence of an irreducible Boolean matrix. Linear Algebra Appl. 97 (1987), 185–210.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Y. Shao, Q. Li: The index set for the class of irreducible Boolean matrices with given period. Linear and Multilinear Algebra 22 (1988), 285–303.

    MATH  MathSciNet  Google Scholar 

  8. R. A. Brualdi, B. L. Liu: Fully indecomposable exponents of primitive matrices. Proc. Amer. Math. Soc. 112 (1991), 1193–1202.

    Article  MATH  MathSciNet  Google Scholar 

  9. X. J. Wu, J. Y. Shao: The index set of convergence of irreducible Boolean matrices. J. Math. Res. Exposition 12 (1992), 441–447. (In Chinese.)

    MATH  MathSciNet  Google Scholar 

  10. J. Y. Shao: On the indices of convergence of irreducible and nearly reducible Boolean matrices. Acta Math. Appl. Sinica 15 (1992), 333–344. (In Chinese.)

    MATH  MathSciNet  Google Scholar 

  11. Y. J. Tan: The semigroup of Hall matrices over a distributive lattice. Semigroup Forum 61 (2000), 303–314.

    Article  MATH  MathSciNet  Google Scholar 

  12. Y. J. Tan: Primitive lattice matrices. Southeast Asian Bull. Math.. To appear.

  13. Y. J. Tan: On compositions of lattice matrices. Fuzzy Sets and Systems 129 (2002), 19–28.

    Article  MATH  MathSciNet  Google Scholar 

  14. Y. Giveón: Lattice matrices. Information and Control 7 (1964), 477–484.

    Article  MATH  MathSciNet  Google Scholar 

  15. K. H. Kim: Boolean Matrix Theory and Applications. Marcel Dekker, New York, 1982.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Fuzhou University, Fuzhou, 350002, P.R. China

    Yi-jia Tan

Authors
  1. Yi-jia Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tan, Yj. Indecomposable matrices over a distributive lattice. Czech Math J 56, 299–316 (2006). https://doi.org/10.1007/s10587-006-0019-3

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10587-006-0019-3

Keywords

Search

Navigation