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On \(Q_r\)-ordered semigroups

open access: yes
Summary: Ordered semigroups in which every proper right ideal is a power joined subsemigroup, namely \(Q_r\)-ordered semigroups, are investigated. We also give characterizations of archimedean weakly commutative \(Q_r\)-ordered semigroups.
Summaprab, P., Sarasit, N.
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Inverse ordered semigroups

open access: yesTurkish Journal of Mathematics
Summary: An element \(x\) of an ordered semigroup \((S, \cdot, \leq)\) is called an inverse element of \(\alpha\in S\) if \(\alpha \leq x\alpha x\) and \(x \leq x\alpha x\). In inverse ordered semigroup is an ordered semigroup \(S\) for which every element of \(S\) possesses an inverse element and the inverse elements of any element of \(S\) are in the
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On intra-regular ordered semigroups

open access: yesSemigroup Forum, 1993
The author continues her studies of partially ordered semigroups \(S\) which are intraregular, that is, for every \(a\in S\) there are \(x,y\in S\) such that \(a\leq xa^ 2 y\) [see the author, Semigroup Forum 44, 341-346 (1992; Zbl 0756.06008)]. It is shown (similar to the purely semigroup theoretical case) that a p.o.
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Idempotent ordered semigroup

open access: yes, 2017
An element e of an ordered semigroup $(S,\cdot,\leq)$ is called an ordered idempotent if $e\leq e^2$. We call an ordered semigroup $S$ idempotent ordered semigroup if every element of $S$ is an ordered idempotent. Every idempotent semigroup is a complete semilattice of rectangular idempotent semigroups and in this way we arrive to many other important ...
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