Boolean Groups

Irving Anellis, Universitätsbibliothek Braunschweig
1982
groups are constructed as equivalence c1asses from elements of Boolean algebra (A,u,n,~,-) associated to the elements of the sequence of natural numbers whose model is N = < 0,0), + , . >, where apartition modulo-m is a subc1ass defined on the Boolean equivalence and congruence relation IN defining NmcA/ lJ with IN associated with identity. This gives a Boolean algebra 91, whose groups, then, are not multiplicative sets, but c1asses of rn-partition subc1asses of the model N_of the Boolean
more » ... se V~ defining the algebra 91. Thus, a Boolean group for 91 with universe V~ may be either an additive or a multiplicative c1ass. These Boolean groups are c10sely related to the .t-groups constructed in Birkhoff's Lattice Theory.
doi:10.24355/dbbs.084-201307091041-0 fatcat:smr4w4i43zgtjdjhd44spocalm