On the cardinal of the linear stable orders in a class of semigroups

A. Baxhaku and M. Aslanski
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 6, 2000, Number 2, Pages 56—60
Download full paper: PDF, 209 Kb


Authors and affiliations

A. Baxhaku
Faculty of Natural Sciences,
University, Tirana

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


The main results are: Theorem 1: For any semigroup S generated by the non-idempotent elements x_1, x_2, ..., x_n and the generating relations (i) x_i x_j = x_j^2; (ii) x_j^2 = x_j^3  and (3) x_i^2 \neq  x_j^2 for i \neq j  there exist n!2^{n-1} non dual two-sided stable orders and \frac{1}{2}[(2n)! - n!2n] (non dual) one sided stable orders which are not two sided stable ones and Theorem 2: Let S’ be a semigroup generated by the idempotents x_1, x_2, ..., x_k,  the non-idempotents x_{k+1}, x_{k+2}, ..., x_n and the relations (i),(ii),(iii). Then the semigroup S’ has n!2^{n-k-1} non-dual two-sided stable orders and \frac{1}{2}[(2n - k)! -n!2^{n-k}] only one-sided stable orders which are not two-sided stable ones.


  1. Baxhaku Artur, On the one-sided orders in semigroups, To appear in Comptes rendus Bulg. Akad. Nauk 5…
  2. Bijev, G., and Todorov, K.,Idempotent-generated subsemigroups of the symmetric semigroup of degree four: computer investigations, Semigroup Forum, Vol. 31 (1985) 119- 122.
  3. Clifford, A.H. and Preston, G.B. The algebraic theory of semigroups, Math. Surveys, Nr.7, Amer. Math. Soc. Providence, R.I. 1961.
  4. Gabovich, E., Totally ordered semigroups and their applications (Russian), Uspehi Mat.Nauk 31(1976), no. 1(187), 137-201.
  5. Jordjev, K., and Todorov, K., On the total orderability of finite semigroups, Mathematics and Education in Mathematics, 1985, 258-262 (Bulgarian, English summary).
  6. Todorov, K., On the linear orderability of two classes of finite semigroups, Semigroup Forum, Vol 45(1992) 71-76.
  7. Saito, T., Ordered idempotent semigroups, J. Math. Soc. Japan. 4 (1962),150-169.

Related papers

Cite this paper

Baxhaku, A. & Aslanski, M. (2000). On the cardinal of the linear stable orders in a class of semigroups. Notes on Number Theory and Discrete Mathematics, 6(2), 56-60.

Comments are closed.