Bernhardt, Robert

uncg

There are 7 item/s.

TitleDateViewsBrief Description
A generalization of torsion to modules 1971 48 The concepts of torsion and torsion-free objects have their origins in abelian group theory, where for an abelian group G the torsion subgroup T(G) of G is defined by T(G) = {x ? G | there exists a positive integer n such that nx = 0}, and where G is...
On rational extensions of a ring 1971 11 The purpose of this paper is to examine the rational extensions of a ring and to prove that under certain conditions the injective hull of a ring is a right self-injective, von Neumann ring. Furthermore, we shall show that the module structure of the...
On quasi-injective abelian groups 1971 13 It is a well-known theorem that any abolian group G satisfying G = nG for every positive integer n is a direct summand of every abelian group H which contains G as a subgroup. Baer (2) generalized this concept to what he called "abelian groups admitt...
Fundamental properties of near-rings 1973 7 The basic properties of near-rings are examined, and are then used to develop several fundamental theorems, among which are the Factor Theorem, the Isomorphism Theorems, the Correspondence Theorem, and theorems concerning near-ring embeddings. Furthe...
On hereditary torsion theories 1973 12 This thesis deals with S. E. Dickson's concept of a hereditary torsion theory for the category RM of left R-modules over an arbitrary ring R. It is proved that a class of left R-modules is a hereditary torsion class if and only if there is an injecti...
Analogies to the Cantor-Schro┬Ęder-Bernstein theorem 1973 3 Let A and B be sets, let f be a one-to-one function from A into B, and let g be a one-to-one function from B into A. The Cantor-Schroder-Bernstein Theorem states that there exists a one-to-one function h from A onto B. This theorem is well known, and...
On purity in abelian groups and in modules 1973 10 The purpose of this thesis is to study the elementary properties of pure subgroups of an abelian group, to use these properties to prove the Fundamental Theorem of Finitely Generated Abelian Groups, and to generalize the abelian group concept of puri...