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Articles 31 - 33 of 33
Full-Text Articles in Algebra
Homogeneous Gorenstein Ideals And Boij Söderberg Decompositions, Sema Güntürkün
Homogeneous Gorenstein Ideals And Boij Söderberg Decompositions, Sema Güntürkün
Theses and Dissertations--Mathematics
This thesis consists of two parts. Part one revolves around a construction for homogeneous Gorenstein ideals and properties of these ideals. Part two focuses on the behavior of the Boij-Söderberg decomposition of lex ideals.
Gorenstein ideals are known for their nice duality properties. For codimension two and three, the structures of Gorenstein ideals have been established by Hilbert-Burch and Buchsbaum-Eisenbud, respectively. However, although some important results have been found about Gorenstein ideals of higher codimension, there is no structure theorem proven for higher codimension cases. Kustin and Miller showed how to construct a Gorenstein ideals in local Gorenstein rings starting …
Homological Algebra With Filtered Modules, Raymond Edward Kremer
Homological Algebra With Filtered Modules, Raymond Edward Kremer
Theses and Dissertations--Mathematics
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.
Algebraic Properties Of Formal Power Series Composition, Thomas S. Brewer
Algebraic Properties Of Formal Power Series Composition, Thomas S. Brewer
Theses and Dissertations--Mathematics
The study of formal power series is an area of interest that spans many areas of mathematics. We begin by looking at single-variable formal power series with coefficients from a field. By restricting to those series which are invertible with respect to formal composition we form a group. Our focus on this group focuses on the classification of elements having finite order. The notion of a semi-cyclic group comes up in this context, leading to several interesting results about torsion subgroups of the group. We then expand our focus to the composition of multivariate formal power series, looking at similar …