On the one-sided orderability for semigroups

A. Baxhaku and M. Aslanski
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 6, 2000, Number 2, Pages 45—55
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Authors and affiliations

A. Baxhaku
Faculty of Natural Sciences,
University, Tirana

M. Aslanski
Faculty of Natural Sciences
South-West University-Blagoevgrad, Bulgaria

Abstract

In the papers of Merlier [5] and Saito [7] there are given some necessary and sufficient conditions on the linear orderability of the bands. Similar questions on semigroups are treated by Jordjev, Todorov [4] and Todorov [9]. In the last paper there are studied for the first time the one-sided orderable semigroups. We considerably enlarge the last studies, giving conditions under which a given semigroup should not be linearly orderable, (being perhaps left or right stable orderable) and conditions when a semigroup is not one sided orderable, or when it is no-one-sided orderable.

References

  1. Bijev, G., and Todorov, K.,Idempotent-generated subsemigroups of the symmetric semigroup of degree four: computer investigations, Semigroup Forum, Vol. 31 (1985) 119- 122.
  2. Clifford, A.H. and Preston, G.B. The algebraic theory of semigroups, Math. Surveys, Nr.7, Amer. Math. Soc. Providence, R.I. 1961.
  3. Gabovich, E., Totally ordered semigroups and their applications (Russian), Uspehi Mat.Nauk 31(1976), no. 1(187), 137-201.
  4. Jordjev, K., and Todorov, K., On the total orderability of finite semigroups, Mathematics and Education in Mathematics, 1985, 258-262 (Bulgarian, English summary).
  5. Merlier,Th., Sur les cr-bandes finies et les demi-groupes totalment ordonnes a-simple, Semigroup Forum Vol 4(1972), 124-149.
  6. Plemmons,R., Cayley tables for all the semigroups of order < 6.
  7. Saito,T., The orderability of idempotent semigroups, Semigroup Forum, Vol 7(1974), 264-285.
  8. Schein, B.M., Problem 8, Semigroup Forum 1 (1970), 90-92.
  9. Todorov, K., On the linear orderability of two classes of finite semigroups, Semigroup Forum, Vol 45(1992) 71-76.
  10. Zibina,L.D., Semigroups where every order is two-sided stable, (Russian) Selected questions of contemporary mathematics, (Ped. Inst. of Leningrad, Hertzen), Leningrad, 1967.70-76.

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Cite this paper

Baxhaku, A. & Aslanski, M. (2000). On the one-sided orderability for semigroups. Notes on Number Theory and Discrete Mathematics, 6(2), 45-55.

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