Prim-algebraic Domains PDF Download
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Author: Michael Huth
Publisher:
ISBN:
Category : Lambda calculus
Languages : en
Pages : 20
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Book Description
Every bounded complete dcpo D with bottom has a prim-algebraic quotient D. We prove that [formula] is a retract of [formula] in PRIME. Let dSCOTT be the category of distributive Scott-domains with maps preserving all non-empty suprema. We show that PRIME is the maximal cartesian closed category in dSCOTT."
Author: Michael Huth
Publisher:
ISBN:
Category : Lambda calculus
Languages : en
Pages : 20
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Book Description
Every bounded complete dcpo D with bottom has a prim-algebraic quotient D. We prove that [formula] is a retract of [formula] in PRIME. Let dSCOTT be the category of distributive Scott-domains with maps preserving all non-empty suprema. We show that PRIME is the maximal cartesian closed category in dSCOTT."
Author: Robert M. Fossum
Publisher: Springer Science & Business Media
ISBN: 3642884059
Category : Mathematics
Languages : en
Pages : 157
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Book Description
There are two main purposes for the wntmg of this monograph on factorial rings and the associated theory of the divisor class group of a Krull domain. One is to collect the material which has been published on the subject since Samuel's treatises from the early 1960's. Another is to present some of Claborn's work on Dedekind domains. Since I am not an historian, I tread on thin ice when discussing these matters, but some historical comments are warranted in introducing this material. Krull's work on finite discrete principal orders originating in the early 1930's has had a great influence on ring theory in the suc ceeding decades. Mori, Nagata and others worked on the problems Krull suggested. But it seems to me that the theory becomes most useful after the notion of the divisor class group has been made func torial, and then related to other functorial concepts, for example, the Picard group. Thus, in treating the group of divisors and the divisor class group, I have tried to explain and exploit the functorial properties of these groups. Perhaps the most striking example of the exploitation of this notion is seen in the works of I. Danilov which appeared in 1968 and 1970.
Author: Marco Fontana
Publisher: Springer
ISBN: 1493909258
Category : Mathematics
Languages : en
Pages : 372
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Book Description
This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non- Noetherian ring theory as well as integer-valued polynomials and functions. Specific topics include: · Homological dimensions of Prüfer-like rings · Quasi complete rings · Total graphs of rings · Properties of prime ideals over various rings · Bases for integer-valued polynomials · Boolean subrings · The portable property of domains · Probabilistic topics in Intn(D) · Closure operations in Zariski-Riemann spaces of valuation domains · Stability of domains · Non-Noetherian grade · Homotopy in integer-valued polynomials · Localizations of global properties of rings · Topics in integral closure · Monoids and submonoids of domains The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees of the conference in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Graz conference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere.
Author: Susumu Oda
Publisher: CRC Press
ISBN: 1584888520
Category : Mathematics
Languages : en
Pages : 298
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Book Description
Although there are many types of ring extensions, simple extensions have yet to be thoroughly explored in one book. Covering an understudied aspect of commutative algebra, Simple Extensions with the Minimum Degree Relations of Integral Domains presents a comprehensive treatment of various simple extensions and their properties. In particular, it ex
Author: P.M. Cohn
Publisher: CRC Press
ISBN: 1351086480
Category : Mathematics
Languages : en
Pages : 154
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Book Description
This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for both using E Artin's legant approach, via valuations. Number Theory is pursued as far as the unit theorem and the finiteness of the class number. In function theory the aim is the Abel-Jacobi theorem describing the devisor class group, with occasional geometrical asides to help understanding. Assuming only an undergraduate course in algebra, plus a little acquaintance with topology and complex function theory, the book serves as an introduction to more technical works in algebraic number theory, function theory or algebraic geometry by an exposition of the central themes in the subject.
Author: Walter R. Cleaveland
Publisher: Springer Science & Business Media
ISBN: 9783540558224
Category : Mathematics
Languages : en
Pages : 596
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Book Description
This book contains a selection of research papers describing recent advancesin the theory of concurrent systems and their applications. The papers were all presented at the CONCUR '92 conference, which has emerged as the premiere conference on formal aspects of concurrency. The authors include such prominent researchers as R. Milner, A. Pnueli, N. Lynch, and V.R. Pratt. The results represent advances in the mathematical understanding of the behavior of concurrent systems: topics covered include process algebras, models of true concurrency, compositional verification techniques, temporal logic, verification case studies, models of probabilistic and real-time systems, models of systems with dynamic structure, and algorithms and decidability results for system analysis. A key feature of CONCUR is its breadth: in one volume it presents a snapshot of the state of the art in concurrency theory. Assuch, it is indispensible to researchers - and would-be researchers - in theformal analysis of concurrent systems.
Author: Thomas W. Hungerford
Publisher: Springer Science & Business Media
ISBN: 9780387905181
Category : Mathematics
Languages : en
Pages : 536
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Book Description
Finally a self-contained, one volume, graduate-level algebra text that is readable by the average graduate student and flexible enough to accommodate a wide variety of instructors and course contents. The guiding principle throughout is that the material should be presented as general as possible, consistent with good pedagogy. Therefore it stresses clarity rather than brevity and contains an extraordinarily large number of illustrative exercises.
Author: Sophie Tison
Publisher: Springer Science & Business Media
ISBN: 9783540578796
Category : Computers
Languages : en
Pages : 374
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Book Description
This volume contains the papers selected for presentation at the 19th Colloquium on Trees in Algebra and Programming (CAAP '94), which was held jointly with the fifth European Symposium on Programming (ESOP '94) in Edinburgh in April 1994. Originally this colloquium series was devoted to the algebraic and combinatorial properties of trees, and their role in various fields of computer science. Taking into account the evolution of computer science, CAAP '94 focuses on logical, algebraic and combinatorial properties of discrete structures (strings, trees, graphs, etc.); the topics also include applications to computer science provided that algebraic or syntactic methods are involved. The volume contains 21 papers selected from 51 submissions as well as two invited papers.
Author: Daniel Anderson
Publisher: Routledge
ISBN: 1351448943
Category : Mathematics
Languages : en
Pages : 448
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Book Description
The contents in this work are taken from both the University of Iowa's Conference on Factorization in Integral Domains, and the 909th Meeting of the American Mathematical Society's Special Session in Commutative Ring Theory held in Iowa City. The text gathers current work on factorization in integral domains and monoids, and the theory of divisibility, emphasizing possible different lengths of factorization into irreducible elements.
Author: Sukumar Das Adhikari
Publisher: CRC Press
ISBN: 9780849309908
Category : Mathematics
Languages : en
Pages : 176
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Book Description
This is an elementary introduction to algebra and number theory. The text begins by a review of groups, rings, and fields. The algebra portion addresses polynomial rings, UFD, PID, and Euclidean domains, field extensions, modules, and Dedckind domains. The number theory portion reviews elementary congruence, quadratic reciprocity, algebraic number fields, and a glimpse into the various aspects of that subject. This book could be used as a one semester course in graduate mathematics.
