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arXiv · 1510.00927

A note on the relation $\mathcal{J}$ in $le$-semigroups

Aida Shasivari·Elton Pasku
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Abstract

We prove that if $S$ is a $le$-semigroup in which left ideal elements commute (condition which is called $\mathbfΛ$), then any $\mathcal{J}$-class satisfying the Green condition is a subsemigroup of $S$. As a corollary of this we show that semisimple $le$-semigroups satisfying $\mathbfΛ$ are precisely those that decompose as a semilattice of left simple $\vee e$-semigroups which are in addition semisimple, intra-regular and satisfy $\mathbfΛ$.

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Aida Shasivari, Elton Pasku. 2015-10-04. A note on the relation $\mathcal{J}$ in $le$-semigroups. https://arxiv.org/abs/1510.00927

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