Recent zbMATH articles in MSC 20M10https://zbmath.org/atom/cc/20M102024-03-13T18:33:02.981707ZWerkzeugOn spined product decompositions of completely regular semigroupshttps://zbmath.org/1528.201022024-03-13T18:33:02.981707Z"Debnath, R."https://zbmath.org/authors/?q=ai:debnath.ramlal|debnath.rajib|debnath.rameswar|debnath.ronit"Bhuniya, A. K."https://zbmath.org/authors/?q=ai:bhuniya.arun-k|bhuniya.anjan-kumar|bhuniya.anjan-krSummary: Here, we have considered two equivalence relations \(\lambda_\ell\) and \(\lambda_r\) that are congruences on regular orthogroups but not on completely regular semigroups, in general. The congruence openings \(\lambda_\ell^o\) and \(\lambda_r^o\) of \(\lambda_\ell\) and \(\lambda_r\), respectively, induce new subvarieties \(\mathcal{V}_{\lambda_\ell^o}, \mathcal{V}^{\lambda_\ell^o}, \mathcal{V}_{\lambda_r^o}, \mathcal{V}^{\lambda_r^o}, \mathcal{V}_{\mathcal{Q}}\) and \(\mathcal{V}^{\mathcal{Q}}\) for every \(\mathcal{V}\in \mathcal{L}(\mathcal{CR})\); and are such that \(\mathcal{V}= \mathcal{V}_{\lambda_\ell^o}\vee \mathcal{V}_{\lambda_r^o}\) and \(\mathcal{V}^{\mathcal{Q}}= \mathcal{V}^{\lambda_\ell^o}\vee \mathcal{V}^{\lambda_r^o} \). The decompositions of an arbitrary completely regular semigroup which are presented here generalize several spined product decompositions for particular classes of completely regular semigroups already given by several authors [\textit{M. Petrich} and \textit{N. R. Reilly}, Completely regular semigroups. Chichester: Wiley (1999; Zbl 0967.20034)], and thus contributes to a unification of the theory.