# Accession Number:

## AD0620447

# Title:

## BAER RINGS AND LINEAR TRANSFORMATIONS.

# Descriptive Note:

## Master's thesis,

# Corporate Author:

## NORTH CAROLINA STATE UNIV RALEIGH

# Personal Author(s):

# Report Date:

## 1965-01-01

# Pagination or Media Count:

## 29.0

# Abstract:

The first five sections of this thesis are devoted to proving that the ring of all nxn triangular matrices over any field, which is not necessarily commutative, belong to the class of Baer rings, for any finite n. The term Baer ring is used to denote those rings in which the left right annihilator of each subset is a principal left right ideal generated by an element, say e, in the ring, with the property e . e e. The sixth section is devoted to proving that in a Baer ring certain ideals, called right and left singular ideals, contain no non-zero elements. The left right singular ideal of a ring is a set of elements of the ring whose left right annihilators have a non-zero intersection with each non-zero left right ideal of the ring. Some indications of why these proofs are significant, a summary of the thesis, and remarks on possible extensions of this work, are the contents of the seventh section. Author