The Module of Pseudo-rational Relations of a Quotient Divisible Group

non-divisibility for abelian groups

Throughout all groups are abelian. We say a group G is n-divisible if nG = G. If G has no non-zero n-divisible subgroups for all n>1 then we say that G is absolutely non-divisible. In the study of class C consisting   all absolutely non-divisible groups such as G, we come across the sub groups T_p(G) = the sum of all p-divisible subgroups and rad_p(G) = the intersection of all p^nG. The proper...

Ranks of modules relative to a torsion theory

Relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $M$, called {em $tau$-rank of} $M$, which coincides with the reduced rank of $M$ whenever $tau$ is the Goldie torsion theory. It is shown that the $tau$-rank of $M$ is measured by the length of certain decompositions of the $tau$-injective hull of $M$. Moreover, some relations between the $tau$-rank of $M$ and c...

Differential Invariant Algebras of Lie Pseudo–Groups

The goal of this paper is to describe, in as much detail as possible, the structure of the algebra of differential invariants of a Lie pseudo-group. Under the assumption of local freeness of the prolonged pseudo-group action, we develop algorithms for locating a finite generating set of differential invariants, establishing the recurrence relations for the differentiated invariants, and fixing ...

Galois actions on torsion points of universal one-dimensional formal modules

Let F be a local non-Archimedean field with ring of integers o and uniformizer ̟. Let X be a one-dimensional formal o-module of F -height n over the algebraic closure F of the residue field of o. By the work of Drinfeld, the universal deformation X of X is a formal group over a power series ring R0 in n − 1 variables over the completion of the maximal unramified extension ônr of o. For h ∈ {0, ....

Characterizing the Multiplicative Group of a Real Closed Field in Terms of its Divisible Maximal Subgroup