The injective envelope of the n x n upper triangular matrix ring over a field

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Elizabeth Edith Bray (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site:
E. E. Posey

Abstract: The purpose of this thesis is to prove that the full n x n matrix ring over a field F is the injective envelope of the upper triangular n x n matrix ring over F. In order that this paper be self-contained, Chapter II is devoted to the basic definitions and properties of modules. However, it has been assumed that the reader has a knowledge of the basic properties of groups and rings. Known theorems have been stated without proof but with a reference as to where the reader may find a proof. Injective modules and essential submodules are discussed in Chapter III, and some distinctive properties of injective modules are developed. This discussion culminates in showing that with certain restrictions we have a characterization of injective modules, due to K. A. Byrd [Theorem 3.12], that to our knowledge is not found in the literature.

Additional Information

Language: English
Date: 1970
Injective modules (Algebra)
Matrix rings

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