In diesem Beitrag wird die Detektion und messtechnische Erfassung der Gletscher-bewegung (Oberflachendeformation) der Pasterze (Glocknergruppe, Hohe Tauern,Kaatzt werden.

摘要

If the free algebra F on one generator in a variety V of algebras (in the sense ofuniversal algebra) has a subalgebra free on two generators, must it also have asubalgebra free on three generators? In general, no; but yes if F generates thevariety V.Generalizing the argument, it is shown that if we are given an algebra andsubalgebras, A_0 )... ) A_n, in a prevariety (SP-closed class of algebras) P suchthat A_n generatesP,and also subalgebrasB_i A_(i-1) (0 0 the subalgebra of A_(i-1)generated by A; andB,is their coproduct inP,then the subalgebra of A generated by B_1, ... , B_n is the coproduct in P of thesealgebras. Some further results on coproducts are noted: If P satisfies the amalgamation property, then one has the stronger "transitiv-ity” statement, that if A has a finite family of subalgebras (B_i,)∈I such that thesubalgebra of A generated by the B_i, is their coproduct, and each B_i; has a finitefamily of subalgebras (c_(iJ))_j∈J_i; with the same property, then the subalgebra of Agenerated by all the C_(ij) is their coproduct. For P a residually small prevariety or an arbitrary quasivariety, relationshipsare proved between the least number of algebras needed to generate P as a pre-variety or quasivariety, and behavior of the coproduct operation in P. It is shown by example that for B a subgroup of the group S = Sym(Ω) ofall permutations of an infinite set Q, the group S need not have a subgroup iso-morphic over B to the coproduct with amalgamation S ∪_BS. But under variousadditional hypotheses on B, the question remains open.