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We investigate to what extent an abelian group G is determined by the homomorphism groups Hom(G;B )w here Bis chosen from a setX of abelian groups. In particular, we address Problem 34 in Professor Fuchs' book which asks ifX can be... more
We investigate to what extent an abelian group G is determined by the homomorphism groups Hom(G;B )w here Bis chosen from a setX of abelian groups. In particular, we address Problem 34 in Professor Fuchs' book which asks ifX can be chosen in such a way that the homomorphism groups determine G up to isomorphism. We show that there is a negative answer to this question. On the other hand, there is a set X which determines the torsion-free groups of nite rank up to quasi-isomorphism.
... Using Theo-rem 2.2 b), a standard argument shows that QA is flat over QR if and only if - @QR QA is exact relative to all sequences 0 + J + QR + QR/J + 0 where J is a right ideal J of QR. ... Hence, yio E QN for each i. Thus t = Ci... more
... Using Theo-rem 2.2 b), a standard argument shows that QA is flat over QR if and only if - @QR QA is exact relative to all sequences 0 + J + QR + QR/J + 0 where J is a right ideal J of QR. ... Hence, yio E QN for each i. Thus t = Ci yio(zio) E A n QNA = (NA). ...
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Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. ... This paper has been... more
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. ... This paper has been digitized, optimized for electronic delivery ...
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This paper shows that Ext R 1 (M,A) is torsion-free whenver A is a rank-1 module over a Dedekind domain R and M is a finite rank torsion-free R-module with R A (M)=0.
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... Using Theo-rem 2.2 b), a standard argument shows that QA is flat over QR if and only if - @QR QA is exact relative to all sequences 0 + J + QR + QR/J + 0 where J is a right ideal J of QR. ... Hence, yio E QN for each i. Thus t = Ci... more
... Using Theo-rem 2.2 b), a standard argument shows that QA is flat over QR if and only if - @QR QA is exact relative to all sequences 0 + J + QR + QR/J + 0 where J is a right ideal J of QR. ... Hence, yio E QN for each i. Thus t = Ci yio(zio) E A n QNA = (NA). ...
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ABSTRACT This paper provides two new characterizations of RM-domains, i.e. domains satisfying the restricted minimum condition. A Noetherian domain is a RM-domain if and only if every torsion module is a direct sum of submodules whose... more
ABSTRACT This paper provides two new characterizations of RM-domains, i.e. domains satisfying the restricted minimum condition. A Noetherian domain is a RM-domain if and only if every torsion module is a direct sum of submodules whose cyclic submodules have finite length and homogeneous composition series. We show that this occurs exactly if all self-small torsion modules are finitely generated.
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ABSTRACT This paper presents a Warfield-type characterization of A-reflexive groups in the case that A is a mixed abelian group of torsion-free rank 1.
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ABSTRACT An abelian group A is quotient divisible if its torsion subgroup tA is reduced, and it contains a finitely generated free subgroup F such that A/F is the direct sum of a finite and a divisible torsion group. This paper focuses on... more
ABSTRACT An abelian group A is quotient divisible if its torsion subgroup tA is reduced, and it contains a finitely generated free subgroup F such that A/F is the direct sum of a finite and a divisible torsion group. This paper focuses on homological properties of quotient divisible groups. A group A such that tA is reduced is quotient divisible if and only if it is small with respect to the class of quotient divisible groups. Further results investigate when an A-generated torsion group is A-solvable. The last section discusses quotient divisible groups A such that ℚ ⊗ℤ E(A)/tE(A) is a quasi-Frobenius ring.
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ABSTRACT An abelian group A is an S-group (S -group) if every subgroup B ≤ A of finite index is A-generated (A-solvable). This article discusses some of the differences between torsion-free S-groups and mixed S-groups, and studies (mixed)... more
ABSTRACT An abelian group A is an S-group (S -group) if every subgroup B ≤ A of finite index is A-generated (A-solvable). This article discusses some of the differences between torsion-free S-groups and mixed S-groups, and studies (mixed) S- and S -groups, which are self-small and have finite torsion-free rank.