Factor-splitting Abelian groups of finite rank
Generalized Almost Completely Decomposable Groups
Generalized Dieudonné and Honda criteria for primary Abelian groups.
Generalized Dieudonné criterion.
Groups qui reflètent les décompositions de leurs quotients ou de leurs sous-groups
Gruppi monotóni di successioni intere
Homology and Direct Sums of Countable Abelian Groups.
Homomorphisms between -projective Abelian groups and left Kasch-rings
Glaz and Wickless introduced the class of mixed abelian groups which have finite torsion-free rank and satisfy the following three properties: i) is finite for all primes , ii) is isomorphic to a pure subgroup of , and iii) is torsion. A ring is a left Kasch ring if every proper right ideal of has a non-zero left annihilator. We characterize the elements of such that is a left Kasch ring, and discuss related results.
Indecomposable (1,3)-groups and a matrix problem
Almost completely decomposable groups with a critical typeset of type and a -primary regulator quotient are studied. It is shown that there are, depending on the exponent of the regulator quotient , either no indecomposables if ; only six near isomorphism types of indecomposables if ; and indecomposables of arbitrary large rank if .
Isomorphism of modular group algebras of direct sums of torsion-complete abelian -groups
Isomorphisms of Direct Products of Cyclic Groups of Prime Power Order
In this paper we formalized some theorems concerning the cyclic groups of prime power order. We formalize that every commutative cyclic group of prime power order is isomorphic to a direct product of family of cyclic groups [1], [18].
Isomorphisms of Direct Products of Finite Commutative Groups
We have been working on the formalization of groups. In [1], we encoded some theorems concerning the product of cyclic groups. In this article, we present the generalized formalization of [1]. First, we show that every finite commutative group which order is composite number is isomorphic to a direct product of finite commutative groups which orders are relatively prime. Next, we describe finite direct products of finite commutative groups
Isomorphisms of Direct Products of Finite Cyclic Groups
In this article, we formalize that every finite cyclic group is isomorphic to a direct product of finite cyclic groups which orders are relative prime. This theorem is closely related to the Chinese Remainder theorem ([18]) and is a useful lemma to prove the basis theorem for finite abelian groups and the fundamental theorem of finite abelian groups. Moreover, we formalize some facts about the product of a finite sequence of abelian groups.
Iterated countable products and sums of the infinite cyclic group
Kappa-Slender Modules
For an arbitrary infinite cardinal , we define classes of -cslender and -tslender modules as well as related classes of -hmodules and initiate a study of these classes.
Martinaxiom und die Beschreibung gewisser Homomorphismen in der Theorie der N1-freien Abelschen Gruppen.
Measurable products of modules
Nice bases for mixed and torsion-free Abelian groups.
Note on Direct Decompositions of Torsion-free Abelian Groups
Number of indecomposable summands in direct decompositions of torsion-free abelian groups