About 2,540 results
|COTORSION-FREE GROUP cotorsion-free Abelian groups. These rings play a |
distinguished role in the realization of rings as endomorphism rings of Abelian
groups. The celebrated theorem of Corner  states that any countable ...
|2. jyi.gLdim.(fl) = oo then there is a cotorsion-free left R-module Af^, such that |
Proof: (1) Let M be a left fi-module of projective dimension 1 < n < oo. ... Now
apply 2.14, 3.10.1, and .2 to produce a group A* € ft(fi) such that proj.dim.(>U) = *.
|If 6 : 0, then the result simply restates the hypothesis that A is cotorsion-free. If 6 : |
7 + 1, then B is cotorsion-free, being an extension of A, by a cotorsion-free group
and B/A,1 is cotorsion-free since the quotient (B /A,,) / (A, /A0,) is cotorsion-free ...
László Fuchs, Rüdiger Göbel, Phillip Schultz - 1989 - Preview
|Let K be a regular, not weakly compact cardinal and S a cotorsion-free, strongly |
homogeneous PID with \S\ < K. Then (a) There exists an E-transitive cotorsion-
free abelian group G, Ni -free and indecomposable as S-module with Cent(End G
|Recall, from V.2.9, that a group A is cotorsion-free if and only if it is reduced, |
torsion-free, and for all primes p, Jp is not embeddable in A. Call a ring R
cotorsion-free if (R, +) is a cotorsion-free group. The problem of characterizing the
|A ring R is the endomorphism ring of some cotorsion-free abelian group if and |
only if R+ is cotorsion-free. The group realizing R can be chosen arbitrarily large.
Recall that an abelian group is cotorsion-free if and only if it has no proper ...
|4.3 Cotorsion-free Groups as Co-local Subgroups The goal of this section is that |
any cotorsion-free group is isomorphic to a co-local subgroup of some cotorsion-
free group. We will utilize a slightly modified Black Box together with a standard ...
|An Abelian group A has no nonzero cotorsion subgroups if A is reduced, |
torsionfree, and has no subgroup « Z(p), the group of p-adic integers, for any
prime p. In this case, A is said to be cotorsion-free. A ring R is cotorsion-free if its
|For a torsion-free reduced algebraically compact group we may take for such a |
system of invariants the set of p-ranks of the group (Section 0) for all ... If there are
no nonzero cotorsion subgroups in a group G then G is called cotorsion-free.
|a reduced torsion-free module M is Matlis cotorsion, if and only if M is R-complete|
, and M is Warfield cotorsion, if and only if M ... Jp ;Q.p// D 0, but Q.p/ is p-divisible,
where J p D R is the ring of p-adic integers and Q.p/ is the group of all rationals ...
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