Generative Complexity In Algebra
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Generative Complexity In Algebra
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Author : Joel Berman
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Generative Complexity In Algebra written by Joel Berman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Considers the behavior of $\mathrm{G}_\mathcal{C}(k)$ when $\mathcal{C}$ is a locally finite equational class (variety) of algebras and $k$ is finite. This title looks at ways that algebraic properties of $\mathcal{C}$ lead to upper or lower bounds on generative complexity.
Generative Complexity In Algebra
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Author : Joel Berman
language : en
Publisher:
Release Date : 2014-09-11
Generative Complexity In Algebra written by Joel Berman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Algebraic varieties categories.
Introduction Background material Part 1. Introducing Generative Complexity: Definitions and examples Semilattices and lattices Varieties with a large number of models Upper bounds Categorical invariants Part 2. Varieties with Few Models: Types 4 or 5 need not apply Semisimple may apply Permutable may also apply Forcing modular behavior Restricting solvable behavior Varieties with very few models Restricting nilpotent behavior Decomposing finite algebras Restricting affine behavior A characterization theorem Part 3. Conclusions: Application to groups and rings Open problems Tables Bibliography
Structural Theory Of Automata Semigroups And Universal Algebra
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Author : Valery B. Kudryavtsev
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-18
Structural Theory Of Automata Semigroups And Universal Algebra written by Valery B. Kudryavtsev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-18 with Mathematics categories.
Several of the contributions to this volume bring forward many mutually beneficial interactions and connections between the three domains of the title. Developing them was the main purpose of the NATO ASI summerschool held in Montreal in 2003. Although some connections, for example between semigroups and automata, were known for a long time, developing them and surveying them in one volume is novel and hopefully stimulating for the future. Another aspect is the emphasis on the structural theory of automata that studies ways to contstruct big automata from small ones. The volume also has contributions on top current research or surveys in the three domains. One contribution even links clones of universal algebra with the computational complexity of computer science. Three contributions introduce the reader to research in the former East block.
The Beilinson Complex And Canonical Rings Of Irregular Surfaces
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Author : Alberto Canonaco
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
The Beilinson Complex And Canonical Rings Of Irregular Surfaces written by Alberto Canonaco and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
An important theorem by Beilinson describes the bounded derived category of coherent sheaves on $\mathbb{P n$, yielding in particular a resolution of every coherent sheaf on $\mathbb{P n$ in terms of the vector bundles $\Omega {\mathbb{P n j(j)$ for $0\le j\le n$. This theorem is here extended to weighted projective spaces. To this purpose we consider, instead of the usual category of coherent sheaves on $\mathbb{P ({\rm w )$ (the weighted projective space of weights $\rm w=({\rm w 0,\dots,{\rm w n)$), a suitable category of graded coherent sheaves (the two categories are equivalent if and only if ${\rm w 0=\cdots={\rm w n=1$, i.e. $\mathbb{P ({\rm w )= \mathbb{P n$), obtained by endowing $\mathbb{P ({\rm w )$ with a natural graded structure sheaf. The resulting graded ringed space $\overline{\mathbb{P ({\rm w )$ is an example of graded scheme (in chapter 1 graded schemes are defined and studied in some greater generality than is needed in the rest of the work). Then in chapter 2 we prove This weighted version of Beilinson's theorem is then applied in chapter 3 to prove a structure theorem for good birational weighted canonical projections of surfaces of general type (i.e., for morphisms, which are birational onto the image, from a minimal surface of general type $S$ into a $3$-dimensional $\mathbb{P ({\rm w )$, induced by $4$ sections $\sigma i\in H0(S,\mathcal{O S({\rm w iK S))$). This is a generalization of a theorem by Catanese and Schreyer (who treated the case of projections into $\mathbb{P 3$), and is mainly interesting for irregular surfaces, since in the regular case a similar but simpler result (due to Catanese) was already known. The theorem essentially states that giving a good birational weighted canonical projection is equivalent to giving a symmetric morphism of (graded) vector bundles on $\overline{\mathbb{P ({\rm w )$, satisfying some suitable conditions. Such a morphism is then explicitly determined in chapter 4 for a family of surfaces with numerical invariant
The Hilbert Function Of A Level Algebra
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Author : A. V. Geramita
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
The Hilbert Function Of A Level Algebra written by A. V. Geramita and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Let $R$ be a polynomial ring over an algebraically closed field and let $A$ be a standard graded Cohen-Macaulay quotient of $R$. The authors state that $A$ is a level algebra if the last module in the minimal free resolution of $A$ (as $R$-module) is of the form $R(-s)a$, where $s$ and $a$ are positive integers. When $a=1$ these are also known as Gorenstein algebras. The basic question addressed in this paper is: What can be the Hilbert Function of a level algebra? The authors consider the question in several particular cases, e.g., when $A$ is an Artinian algebra, or when $A$ is the homogeneous coordinate ring of a reduced set of points, or when $A$ satisfies the Weak Lefschetz Property. The authors give new methods for showing that certain functions are NOT possible as the Hilbert function of a level algebra and also give new methods to construct level algebras. In a (rather long) appendix, the authors apply their results to give complete lists of all possible Hilbert functions in the case that the codimension of $A = 3$, $s$ is small and $a$ takes on certain fixed values.
The Complex Monge Ampere Equation And Pluripotential Theory
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Author : Sławomir Kołodziej
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
The Complex Monge Ampere Equation And Pluripotential Theory written by Sławomir Kołodziej and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
We collect here results on the existence and stability of weak solutions of complex Monge-Ampere equation proved by applying pluripotential theory methods and obtained in past three decades. First we set the stage introducing basic concepts and theorems of pluripotential theory. Then the Dirichlet problem for the complex Monge-Ampere equation is studied. The main goal is to give possibly detailed description of the nonnegative Borel measures which on the right hand side of the equation give rise to plurisubharmonic solutions satisfying additional requirements such as continuity, boundedness or some weaker ones. In the last part, the methods of pluripotential theory are implemented to prove the existence and stability of weak solutions of the complex Monge-Ampere equation on compact Kahler manifolds. This is a generalization of the Calabi-Yau theorem.
Relatively Hyperbolic Groups Intrinsic Geometry Algebraic Properties And Algorithmic Problems
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Author : Denis V. Osin
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Relatively Hyperbolic Groups Intrinsic Geometry Algebraic Properties And Algorithmic Problems written by Denis V. Osin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
In this the authors obtain an isoperimetric characterization of relatively hyperbolicity of a groups with respect to a collection of subgroups. This allows them to apply classical combinatorial methods related to van Kampen diagrams to obtain relative analogues of some well-known algebraic and geometric properties of ordinary hyperbolic groups. There is also an introduction and study of the notion of a relatively quasi-convex subgroup of a relatively hyperbolic group and solve somenatural algorithmic problems.
Higher Complex Torsion And The Framing Principle
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Author : Kiyoshi Igusa
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Higher Complex Torsion And The Framing Principle written by Kiyoshi Igusa and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Intends to prove that higher Franz-Reidemeister (FR) torsion satisfies the transfer property and a formula known as the 'Framing Principle' in full generality. This title uses these properties to compute the higher FR-torsion for various smooth bundles with oriented closed even dimensional manifold fibers.
Hiroakira Ono On Substructural Logics
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Author : Nikolaos Galatos
language : en
Publisher: Springer Nature
Release Date : 2021-12-13
Hiroakira Ono On Substructural Logics written by Nikolaos Galatos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-13 with Philosophy categories.
This volume is dedicated to Hiroakira Ono life’s work on substructural logics. Chapters, written by well-established academics, cover topics related to universal algebra, algebraic logic and the Full Lambek calculus; the book includes a short biography about Hiroakira Ono. The book starts with detailed surveys on universal algebra, abstract algebraic logic, topological dualities, and connections to computer science. It further contains specialised contributions on connections to formal languages (recognizability in residuated lattices and connections to the finite embedding property), covering systems for modal substructural logics, results on the existence and disjunction properties and finally a study of conservativity of expansions. This book will be primarily of interest to researchers working in algebraic and non-classical logic.
The Second Duals Of Beurling Algebras
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Author : Harold G. Dales
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
The Second Duals Of Beurling Algebras written by Harold G. Dales and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Let $A$ be a Banach algebra, with second dual space $A""$. We propose to study the space $A""$ as a Banach algebra. There are two Banach algebra products on $A""$, denoted by $\,\Box\,$ and $\,\Diamond\,$. The Banach algebra $A$ is Arens regular if the two products $\Box$ and $\Diamond$ coincide on $A""$.