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
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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

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.

References

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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.

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