Rocky Mountain Journal of Mathematics

The Lattice of Semilattice-Matrix Decompositions of a Semigroup

Miroslav Ćirić and Stojan Bogdanović

Full-text: Open access

Article information

Source
Rocky Mountain J. Math. Volume 29, Number 4 (1999), 1225-1235.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
http://projecteuclid.org/euclid.rmjm/1181070405

Digital Object Identifier
doi:10.1216/rmjm/1181070405

Mathematical Reviews number (MathSciNet)
MR1743369

Zentralblatt MATH identifier
0973.20054

Citation

Ćirić, Miroslav; Bogdanović, Stojan. The Lattice of Semilattice-Matrix Decompositions of a Semigroup. Rocky Mountain J. Math. 29 (1999), no. 4, 1225--1235. doi:10.1216/rmjm/1181070405. http://projecteuclid.org/euclid.rmjm/1181070405.


Export citation

References

  • G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloq. Pub. 25, 3rd ed., Providence, 1979.
  • S. Bogdanović, Semigroups with a system of subsemigroups, Inst. of Math., Novi Sad, 1985.
  • S. Bogdanović and M. Ćirić, Semigroups, Prosveta, Niš, 1993 (in Serbian).
  • --------, Semilattices of weakly left Archimedean semigroups, FILOMAT (Niš) 9 (1995), 603-610.
  • --------, A note on left regular semigroups, Publ. Math. Debrecen 48 (1996), 285-291.
  • P. Chu, Y.Q. Guo and X.M. Ren, The semilattice (matrix)-matrix(semilattice) decomposition of the quasi-completely orthodox semigroups, Chinese J. Contemp. Math. 10 (1989), 425-438.
  • A.H. Clifford, Semigroups admitting relative inverses, Annals of Math. (2) 42 (1941), 1037-1049.
  • --------, Bands of semigroups, Proc. Amer. Math. Soc. 5 (1954), 499-504.
  • A.H. Clifford and G.B. Preston, The algebraic theory of semigroups, Vol. 1, Amer. Math. Soc., Providence, 1961.
  • D. McLean, General theory of lattices, Akademie-Verlag, Berlin, 1978.
  • --------, Idempotent semigroups, Amer. Math. Monthly 6 (1954), 110-113.
  • M. Petrich, The maximal matrix decomposition of a semigroup, Portugal. Math. 25 (1966), 15-33.
  • --------, Homomorphisms of a semigroup onto normal bands, Acta Sci. Math. (Szeged) 27 (1966), 185-196.
  • --------, Lectures in semigroups, Akademie-Verlag, Berlin, 1977.
  • L.N. Shevrin, Theory of epigroups II, Mat. Sb. 185 (1994), 153-176 (in Russian).