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Cobalanced exact sequences

Anthony Giovannitti, H. Pat Goeters, Claudia Metelli (1989)

Commentationes Mathematicae Universitatis Carolinae

Decompositions of local rigid ACD groups

Adolf Mader, Otto Mutzbauer (2001)

Colloquium Mathematicae

We study direct decompositions of extensions of rigid completely decomposable groups by finite primary groups. These decompositions are unique and can be found by finite procedures. By passing to certain quotients the determination of the direct decompositions is made more efficient.

Direct decompositions of uniform groups

A. Mader, O. Mutzbauer (2001)

Colloquium Mathematicae

Uniform groups are extensions of rigid completely decomposable groups by a finite direct sum of cyclic primary groups all of the same order. The direct decompositions of uniform groups are completely determined by an algorithm that is realised by a MAPLE procedure.

Groupes p -réduits

Marie-Paule Brameret (1962/1963)

Séminaire Dubreil. Algèbre et théorie des nombres

Homomorphisms between A -projective Abelian groups and left Kasch-rings

Ulrich F. Albrecht, Jong-Woo Jeong (1998)

Czechoslovak Mathematical Journal

Glaz and Wickless introduced the class G of mixed abelian groups A which have finite torsion-free rank and satisfy the following three properties: i) A p is finite for all primes p , ii) A is isomorphic to a pure subgroup of Π p A p , and iii) H o m ( A , t A ) is torsion. A ring R is a left Kasch ring if every proper right ideal of R has a non-zero left annihilator. We characterize the elements A of G such that E ( A ) / t E ( A ) is a left Kasch ring, and discuss related results.

Indecomposable (1,3)-groups and a matrix problem

David M. Arnold, Adolf Mader, Otto Mutzbauer, Ebru Solak (2013)

Czechoslovak Mathematical Journal

Almost completely decomposable groups with a critical typeset of type ( 1 , 3 ) and a p -primary regulator quotient are studied. It is shown that there are, depending on the exponent of the regulator quotient p k , either no indecomposables if k 2 ; only six near isomorphism types of indecomposables if k = 3 ; and indecomposables of arbitrary large rank if k 4 .

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