 About 2,540 results  books.google.com COTORSIONFREE GROUP cotorsionfree Abelian groups. These rings play a
distinguished role in the realization of rings as endomorphism rings of Abelian
groups. The celebrated theorem of Corner [1] states that any countable ... 

 books.google.com 2. jyi.gLdim.(fl) = oo then there is a cotorsionfree left Rmodule Af^, such that
Proof: (1) Let M be a left fimodule 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) = *.
2. 

 books.google.com If 6 : 0, then the result simply restates the hypothesis that A is cotorsionfree. If 6 :
7 + 1, then B is cotorsionfree, being an extension of A, by a cotorsionfree group
and B/A,1 is cotorsionfree since the quotient (B /A,,) / (A, /A0,) is cotorsionfree ... 

 books.google.com László Fuchs, Rüdiger Göbel, Phillip Schultz  1989  Preview Let K be a regular, not weakly compact cardinal and S a cotorsionfree, strongly
homogeneous PID with \S\ < K. Then (a) There exists an Etransitive cotorsion
free abelian group G, Ni free and indecomposable as Smodule with Cent(End G
) ... 

 books.google.com Recall, from V.2.9, that a group A is cotorsionfree if and only if it is reduced,
torsionfree, and for all primes p, Jp is not embeddable in A. Call a ring R
cotorsionfree if (R, +) is a cotorsionfree group. The problem of characterizing the
... 

 books.google.com A ring R is the endomorphism ring of some cotorsionfree abelian group if and
only if R+ is cotorsionfree. The group realizing R can be chosen arbitrarily large.
Recall that an abelian group is cotorsionfree if and only if it has no proper ... 

 books.google.com 4.3 Cotorsionfree Groups as Colocal Subgroups The goal of this section is that
any cotorsionfree group is isomorphic to a colocal subgroup of some cotorsion
free group. We will utilize a slightly modified Black Box together with a standard ... 

 books.google.com An Abelian group A has no nonzero cotorsion subgroups if A is reduced,
torsionfree, and has no subgroup « Z(p), the group of padic integers, for any
prime p. In this case, A is said to be cotorsionfree. A ring R is cotorsionfree if its
additive ... 

 books.google.com For a torsionfree reduced algebraically compact group we may take for such a
system of invariants the set of pranks of the group (Section 0) for all ... If there are
no nonzero cotorsion subgroups in a group G then G is called cotorsionfree. 

 books.google.com a reduced torsionfree module M is Matlis cotorsion, if and only if M is Rcomplete
, and M is Warfield cotorsion, if and only if M ... Jp ;Q.p// D 0, but Q.p/ is pdivisible,
where J p D R is the ring of padic integers and Q.p/ is the group of all rationals ... 

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