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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 33 for “"commutative algebra"”.
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The Existence of K-Coefficient Fields in Commutative Algebras
… with the following problem. | Let A be a commutative algebra over a subfield K of characteristic p /= 0. Let N be a maximal ideal of A and g the canonical homomorphism of A onto A/N. Denote A/N by F and identify K and gK. Assume F is pure inseparable over K. When does there exist a field …
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The Combinatorics of Involutive Bases: Theory, algorithms and applications
… monomial ideals and other related structures in commutative algebra. Our primary tool for exploring the connections between these algebraic objects and combinatorics is the use of involutive bases, along with other types of Gröbner bases that exhibit additional combinatorial properties. In …
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Computational Algebraic Geometry Applied to Invariant Theory
Commutative algebra finds its roots in invariant theory and the connection is drawn from a modern standpoint. The Hilbert Basis Theorem and the Nullstellenstatz were considered lemmas for classical invariant theory. The Groebner basis is a modern tool used and is implemented with the computer …
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Gröbner Bases and Syzygy Modules
… bases has become a useful tool in computational commutative algebra. In this paper, we outline some basic results, as they are found in [1], including the concepts of terms ordering, multivariable polynomial division, Gröbner bases, Buchberger's algorithm, and syzygy modules. Specially, we …
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The Existence of Coefficient Field Composites in Commutative Algebras
Let A be a commutative algebra with base field K <= A. Let N be a maximal ideal of A and g the natural K-homomorphism of A onto A/N. We say that A has a coefficient field F for N if there exist a field F<=A such that gF = A/N, g/F (g restricted to F) is one-one and the identities of F and A …
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Representation of non-commutative topological algebras
… theorem enables us to represent a complex commutative C*-algebra as a full algebra of complex valued functions defined on its set of primitive ideals which is called the structure space of the algebra. In is thesis we are concerned with the generalization of this type of representation …
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Geometric, Algebraic, and Topological Connections in the Historical Sphere of the Platonic Solids
… that have connected Euclidean geometry, non-commutative algebra and topology in important ways.
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Betti numbers of Koszul algebras and codimension two matrix factorizations
… projects on the structure of free resolutions in commutative algebra. After developing some necessary background, we prove a structure theorem in Chapter 3 for the defining ideals of Koszul almost complete intersections and, in the process, give an affirmative answer for all such rings to a …
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Splines on polytopal complexes
This thesis concerns the algebra $C^r(\PC)$ of $C^r$ piecewise polynomial functions (splines) over a subdivision by convex polytopes $\PC$ of a domain $\Omega\subset\R^n$. Interest in this algebra arises in a wide variety of contexts, ranging from approximation theory and computer-aided geometric …
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APPROXIMATE GROBNER BASES A BACKWARDS APPROACH
… object of exact computation polynomial algebra, as it answers many of the important questions of commutative algebra, such as ideal membership and computation of the Hilbert polynomial. It is traditionally computed using variants of Buchberger’s algorithm. Here, we take a backwards …
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The syzygy theorem and the weak Lefschetz Property
This thesis consists of two research topics in commutative algebra. In the first chapter, a comprehensive analysis is given of the Weak Lefschetz property in the case of ideals generated by powers of linear forms in a standard graded polynomial ring of characteristic zero. The main point to take …
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Closure Operations on Subgroups
… involving closure operations on the ideals of commutative rings. The most accessible paper on this is written by Neil Epstein, entitled "A Guide to Closure Operations in Commutative Algebra". This paper compiles much of the research done on the topic, and gives the reader an overview of closure …
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Adams Operations and the Dennis Trace Map
For a commutative algebra A, the algebraic K-theory of A, K*(A), and the Hochschild homology of A, HH*(A), are graded rings, and the Dennis trace map D : K *(A) → HH*( A) is a graded ring map. Since Hochschild homology is a more user friendly theory than the algebraic K-theory, one would like …
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Systems, generativity and interactional effects
… that obstruction. We show how to extract algebraic objects (e.g., vectors spaces) from the systems, that encode their generativity: their potential to generate new phenomena upon interaction. Those objects may then be used to link the properties of the interconnected system to its separate …
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The foundations of modern algebra
… by British mathematicians to the 'foundations of algebra' in the first half of the nineteenth century, and to assess the importance of these advances against the inadequacies of eighteenth century algebra and the subsequent development of modern algebra. In order to realize this aim, it was …
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Equivariant Modules
… the appendix of the famous book by D. Eisenbud "Commutative Algebra with a View Towards Algebraic Geometry". This family includes the Eagon-Northcott and Buschsbaum-Rim complexes. Our objective is to study this family, and, in particular, refine the knowledge of its cohomology. First, we obtain …
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Kippenhahn's Conjecture: Counterexamples and Quantisation
Linear pencils are algebraic structures defined by linear polynomials in several real variables,whose coefficients are hermitian matrices. Alternatively, they may be viewed as matrices whose entries are linear polynomials in the variables in question. By requiring that the matrix thus defined be …
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An exploration of near-vector space theory
… in the literature, this thesis provides algebraic proofs of several key results. One such result shows that a subspace of a near-vector space only requires the space to be nonempty and the closure under addition and scalar multiplication. Another fundamental result establishes that the …
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Koszul Complexes, Local Cohomology, Universal Resolutions, and Cohomological Support Varieties
… Within this, we first provide an overview of DG algebras and universal resolutions. We then provide a survey concerning the relationship between some relatively common conditions on module resolutions, namely Golodity and formality, and A-infinity algebras. We go over some of the definitions of …
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Invariant polynomials and machine learning
… them. By borrowing the necessary tools from commutative algebra and invariant theory, we construct systematic methods to obtain sets of invariant variables that describe two such systems: particle physics and physical chemistry. In both cases, our systems are described by a collection of …
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