caa a22 4500 606200762 CHVBK 20210128100945.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s00025-014-0400-8 doi (NATIONALLICENCE)springer-10.1007/s00025-014-0400-8 Petrich Mario 21420 Bol, Brač, Croatia aut On Malcev Products of Normal Cryptogroups [Elektronische Daten] [Mario Petrich] Normal cryptogroups represented as strong semilattices of completely simple semigroups admit a detailed study of their quasivarieties; in particular of their lattices and groupoids under Malcev product. In this context, we construct the lattice of quasivarieties generated by semilattices $${\mathcal{S}}$$ S , groups $${\mathcal{G}}$$ G , and rectangular bands $${\mathcal{RB}}$$ RB ; it is a 17-element distributive lattice. We compute the groupoids of quasivarieties generated by pairs $${(\mathcal{S}, \mathcal{G}), (\mathcal{S},\mathcal{RB})}$$ ( S , G ) , ( S , RB ) , and $${(\mathcal{G},\mathcal{RB})}$$ ( G , RB ) , as well as find the list of quasivarieties which can be expressed by Malcev products with words of length at most equal to 3. This analysis presupposes multiple characterizations of each quasivariety involved in order to establish their relationship, and in particular to prove that all the joins are obtained by means of subdirect products. Springer Basel, 2014 Normal cryptogroup nationallicence normal band nationallicence completely simple semigroup nationallicence subdirect product nationallicence Malcev product nationallicence quasivariety nationallicence strong semilattice nationallicence Results in Mathematics Springer Basel 67/1-2(2015-02-01), 153-176 1422-6383 67:1-2<153 2015 67 25 https://doi.org/10.1007/s00025-014-0400-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00025-014-0400-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Petrich Mario 21420 Bol, Brač, Croatia aut NATIONALLICENCE 773 0- Results in Mathematics Springer Basel 67/1-2(2015-02-01), 153-176 1422-6383 67:1-2<153 2015 67 25