Date Available
5-3-2014
Year of Publication
2014
Degree Name
Doctor of Philosophy (PhD)
Document Type
Doctoral Dissertation
College
Arts and Sciences
Department/School/Program
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.
Recommended Citation
Kremer, Raymond Edward, "HOMOLOGICAL ALGEBRA WITH FILTERED MODULES" (2014). Theses and Dissertations--Mathematics. 18.
https://uknowledge.uky.edu/math_etds/18
