caa a22 4500 445345349 CHVBK 20180317142827.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00233-011-9318-6 doi (NATIONALLICENCE)springer-10.1007/s00233-011-9318-6 Petrich Mario 21420, Bol, Brač, Croatia aut Malcev products of unipotent monoids and varieties of bands [Elektronische Daten] [Mario Petrich] Let $\mathcal{U}$ be the class of all unipotent monoids and $\mathcal{B}$ the variety of all bands. We characterize the Malcev product $\mathcal{U} \circ \mathcal{V}$ where $\mathcal{V}$ is a subvariety of $\mathcal{B}$ low in its lattice of subvarieties, $\mathcal{B}$ itself and the subquasivariety $\mathcal{S} \circ \mathcal{RB}$ , where $\mathcal{S}$ stands for semilattices and $\mathcal{RB}$ for rectangular bands, in several ways including by a set of axioms. For members of some of them we describe the structure as well. This succeeds by using the relation $\widetilde{\mathcal{H}}= \widetilde{\mathcal{L}} \cap \widetilde{\mathcal{R}}$ , where $a\;\,\widetilde{\mathcal{L}}\;\,b$ if and only if a and b have the same idempotent right identities, and $\widetilde{\mathcal{R}}$ is its dual. We also consider $(\mathcal{U} \circ \mathcal{RB}) \circ \mathcal{S}$ which provides the motivation for this study since $(\mathcal{G} \circ \mathcal{RB}) \circ \mathcal{S}$ coincides with completely regular semigroups, where $\mathcal{G}$ is the variety of all groups. All this amounts to a generalization of the latter: $\mathcal{U}$ instead of $\mathcal{G}$ . Springer Science+Business Media, LLC, 2011 Malcev product nationallicence Unipotent monoid nationallicence Quasivariety nationallicence Strong semilattice nationallicence Rectangular band nationallicence Axiom nationallicence Semigroup Forum Springer-Verlag 83/2(2011-10-01), 161-189 0037-1912 83:2<161 2011 83 233 https://doi.org/10.1007/s00233-011-9318-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-011-9318-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Petrich Mario 21420, Bol, Brač, Croatia aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 83/2(2011-10-01), 161-189 0037-1912 83:2<161 2011 83 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer