caa a22 4500 469027061 CHVBK 20180323132732.0 cr unu---uuuuu 170328e19921201xx s 000 0 eng 10.1007/BF01190773 doi (NATIONALLICENCE)springer-10.1007/BF01190773 Kiss Emil Mathematical Institute of the Hungarian Academy of Sciences, P.O.B. 127, 1364, Budapest, Hungary aut Three remarks on the modular commutator [Elektronische Daten] [Emil Kiss] First a problem of Ralph McKenzie is answered by proving that in a finitely directly representable variety every directly indecomposable algebra must be finite. Then we show that there is no local proof of the fundamental theorem of Abelian algebras nor of H. P. Gumm's permutability results. This part may also be of interest for those investigating non-modular Abelian algebras. Finally we provide a Gumm-type characterization of the situation when twonot necessarily comparable congruences centralize each other. In doing this, we introduce a four variable version of the difference term in every modular variety. A "two-terms condition” is also investigated. Birkhäuser Verlag, 1992 algebra universalis Birkhäuser-Verlag 29/4(1992-12-01), 455-476 0002-5240 29:4<455 1992 29 12 https://doi.org/10.1007/BF01190773 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01190773 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kiss Emil Mathematical Institute of the Hungarian Academy of Sciences, P.O.B. 127, 1364, Budapest, Hungary aut NATIONALLICENCE 773 0- algebra universalis Birkhäuser-Verlag 29/4(1992-12-01), 455-476 0002-5240 29:4<455 1992 29 12 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer