# Bernhardt, Robert

## uncg

There are 7 item/s.

Title | Date | Views | Brief 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¨der-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... |