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ORDER-CONGRUENCES ON S-POSETS

XIE XIANG-YUN;SHI XIAOPING

  • Published : 2005.01.01

Abstract

The aim of this paper is to study order-congruences on a S-poset A and to characterize the order-congruences by the concepts of pseudooreders on A and quasi-chains module a congruence p. Some homomorphism theorems of S-posets are given which is similar to the one of ordered semigroups. Finally, It is shown that there exists the non-trivial order-congruence on a S-poset by an example.

Keywords

S-poset;order-congruence;quasi-chain module p;pseudo order

References

  1. S. M. Fakhruddin, Absolute flatness and amalgrams in pomonoids, Semigroup Forum 33 (1986), 15-22 https://doi.org/10.1007/BF02573178
  2. S. M. Fakhruddin, On the category of S-posets, Acta Sci. Math. 52 (1988), 85-92
  3. J. M. Howie, An Introduction to Semigroup Theory, Academic Press, 1976
  4. N. Kehayopulu and M. Tsingelis, On subdirectly irreducible ordered semigroups, Semigroup Forum Semigroup Forum 50 (1995), 161-177 https://doi.org/10.1007/BF02573514
  5. X. Y. Xie, An Introduction to Ordered Semigroup Theory, Beijing, Science Press, 2001
  6. X. Y. Xie, Contributions to theory of congruences on ordered semigroups, Doctoral Dissertation, Lanzhou University, 1995
  7. X. Y. Xie and M. F. Wu, On congruences on ordered semigroups, Math. Japon- ica, 45 (1997), no. 1, 81-85
  8. Z. Liu, S-systems Theory of Semigroups, Beijing, Science Press, 1999
  9. N. Kehayopulu Pseudoorder in ordered semigroups, Semigroup Forum 50 (1995), 389-392

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  4. Perfection for pomonoids vol.81, pp.1, 2010, https://doi.org/10.1007/s00233-010-9237-y
  5. Axiomatisability problems for S-posets vol.82, pp.2, 2011, https://doi.org/10.1007/s00233-010-9273-7