Year of Publication

2014

Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation

College

Arts and Sciences

Department

Mathematics

First Advisor

Dr. Edgar Enochs

Abstract

Classical homological algebra is done in a category of modules beginning with the study of projective and injective modules. This dissertation investigates analogous notions of projectivity and injectivity in a category of filtered modules. This category is similar to one studied by Sjödin, Nǎstǎsescu, and Van Oystaeyen. In particular, projective and injective objects with respect to the restricted class of strict morphisms are defined and characterized. Additionally, an analogue to the injective envelope is discussed with examples showing how this differs from the usual notion of an injective envelope.

Included in

Algebra Commons

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