The Polynomial Identities And Invariants Of N X N Matrices
DOWNLOAD
Download The Polynomial Identities And Invariants Of N X N Matrices PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Polynomial Identities And Invariants Of N X N Matrices book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
The Polynomial Identities And Invariants Of N Times N Matrices
DOWNLOAD
Author : Edward Formanek
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
The Polynomial Identities And Invariants Of N Times N Matrices written by Edward Formanek 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 1991 with Mathematics categories.
The theory of polynomial identities, as a well-defined field of study, began with a well-known 1948 article of Kaplansky. The field has since developed along two branches: the structural, which investigates the properties of rings which satisfy a polynomial identity; and the varietal, which investigates the set of polynomials in the free ring which vanish under all specializations in a given ring. This book is based on lectures delivered during an NSF-CBMS Regional Conference, held at DePaul University in July 1990, at which the author was the principal lecturer. The first part of the book is concerned with polynomial identity rings. The emphasis is on those parts of the theory related to n x n matrices, including the major structure theorems and the construction of certain polynomials identities and central polynomials for n x n matrices. The ring of generic matrices and its centre is described. The author then moves on to the invariants of n x n matrices, beginning with the first and second fundamental theorems, which are used to describe the polynomial identities satisfied by n x n matrices. One of the exceptional features of this book is the way it emphasizes the connection between polynomial identities and invariants of n x n matrices. Accessible to those with background at the level of a first-year graduate course in algebra, this book gives readers an understanding of polynomial identity rings and invariant theory, as well as an indication of current problems and research in these areas.
The Polynomial Identities And Invariants Of N X N Matrices
DOWNLOAD
Author : Edward Formanek
language : en
Publisher:
Release Date : 1991
The Polynomial Identities And Invariants Of N X N Matrices written by Edward Formanek and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Matrices categories.
The theory of polynomial identities, as a well-defined field of study, began with a well-known 1948 article of Kaplansky. The field since developed along two branches: the structural, which investigates the properties of rings that satisfy a polynomial identity; and the varietal, which investigates the set of polynomials in the free ring that vanish under all specializations in a given ring. This book is based on lectures delivered during an NSF-CBMS Regional Conference, held at DePaul University in July 1990, at which the author was the principal lecturer. The first part of the book is concer.
Trends In Ring Theory
DOWNLOAD
Author : Vlastimil Dlab
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Trends In Ring Theory written by Vlastimil Dlab 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 1998 with Mathematics categories.
The Ring Theory Conference, held a the University of Miskolc, Hungary, successfully accomplished its two goals: to reflect contemporary trends in the subject area; and to offer a meeting place for a large number of Eastern European algebraists and their colleagues from around the world. Particular emphasis was placed on recent developments in the following four areas: representation theory, group algebras, PI algebras and general ring theory. This book presents 13 of the invited lectures.
Algebraists Homage Papers In Ring Theory And Related Topics
DOWNLOAD
Author : Shimshon A. Amitsur
language : en
Publisher: American Mathematical Soc.
Release Date : 1982
Algebraists Homage Papers In Ring Theory And Related Topics written by Shimshon A. Amitsur 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 1982 with Mathematics categories.
Polynomial Identities And Asymptotic Methods
DOWNLOAD
Author : A. Giambruno
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Polynomial Identities And Asymptotic Methods written by A. Giambruno 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.
This book gives a state of the art approach to the study of polynomial identities satisfied by a given algebra by combining methods of ring theory, combinatorics, and representation theory of groups with analysis. The idea of applying analytical methods to the theory of polynomial identities appeared in the early 1970s and this approach has become one of the most powerful tools of the theory. A PI-algebra is any algebra satisfying at least one nontrivial polynomial identity. This includes the polynomial rings in one or several variables, the Grassmann algebra, finite-dimensional algebras, and many other algebras occurring naturally in mathematics. The core of the book is the proof that the sequence of co-dimensions of any PI-algebra has integral exponential growth - the PI-exponent of the algebra. Later chapters further apply these results to subjects such as a characterization of varieties of algebras having polynomial growth and a classification of varieties that are minimal for a given exponent.
Representations Of Finite Dimensional Algebras And Related Topics In Lie Theory And Geometry
DOWNLOAD
Author : Vlastimil Dlab
language : en
Publisher: American Mathematical Soc.
Release Date :
Representations Of Finite Dimensional Algebras And Related Topics In Lie Theory And Geometry written by Vlastimil Dlab 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 with Mathematics categories.
These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ''instructional'' workshop preceding the conference, there were also workshops on ''Commutative Algebra, Algebraic Geometry and Representation Theory'', ''Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ''Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.
Polynomial Identities And Combinatorial Methods
DOWNLOAD
Author : Antonio Giambruno
language : en
Publisher: CRC Press
Release Date : 2003-05-20
Polynomial Identities And Combinatorial Methods written by Antonio Giambruno and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-20 with Mathematics categories.
Polynomial Identities and Combinatorial Methods presents a wide range of perspectives on topics ranging from ring theory and combinatorics to invariant theory and associative algebras. It covers recent breakthroughs and strategies impacting research on polynomial identities and identifies new concepts in algebraic combinatorics, invariant and representation theory, and Lie algebras and superalgebras for novel studies in the field. It presents intensive discussions on various methods and techniques relating the theory of polynomial identities to other branches of algebraic study and includes discussions on Hopf algebras and quantum polynomials, free algebras and Scheier varieties.
Notices Of The American Mathematical Society
DOWNLOAD
Author : American Mathematical Society
language : en
Publisher:
Release Date : 1991
Notices Of The American Mathematical Society written by American Mathematical Society and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Graduate Algebra Noncommutative View
DOWNLOAD
Author : Louis Halle Rowen
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Graduate Algebra Noncommutative View written by Louis Halle Rowen 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 2008 with Mathematics categories.
This book is an expanded text for a graduate course in commutative algebra, focusing on the algebraic underpinnings of algebraic geometry and of number theory. Accordingly, the theory of affine algebras is featured, treated both directly and via the theory of Noetherian and Artinian modules, and the theory of graded algebras is included to provide the foundation for projective varieties. Major topics include the theory of modules over a principal ideal domain, and its applications to matrix theory (including the Jordan decomposition), the Galois theory of field extensions, transcendence degree, the prime spectrum of an algebra, localization, and the classical theory of Noetherian and Artinian rings. Later chapters include some algebraic theory of elliptic curves (featuring the Mordell-Weil theorem) and valuation theory, including local fields. One feature of the book is an extension of the text through a series of appendices. This permits the inclusion of more advanced material, such as transcendental field extensions, the discriminant and resultant, the theory of Dedekind domains, and basic theorems of rings of algebraic integers. An extended appendix on derivations includes the Jacobian conjecture and Makar-Limanov's theory of locally nilpotent derivations. Gröbner bases can be found in another appendix. Exercises provide a further extension of the text. The book can be used both as a textbook and as a reference source.
Polynomial Identity Rings
DOWNLOAD
Author : Vesselin Drensky
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Polynomial Identity Rings written by Vesselin Drensky and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A ring R satisfies a polynomial identity if there is a polynomial f in noncommuting variables which vanishes under substitutions from R. For example, commutative rings satisfy the polynomial f(x,y) = xy - yx and exterior algebras satisfy the polynomial f(x,y,z) = (xy - yx)z - z(xy - yx). "Satisfying a polynomial identity" is often regarded as a generalization of commutativity. These lecture notes treat polynomial identity rings from both the combinatorial and structural points of view. The former studies the ideal of polynomial identities satisfied by a ring R. The latter studies the properties of rings which satisfy a polynomial identity. The greater part of recent research in polynomial identity rings is about combinatorial questions, and the combinatorial part of the lecture notes gives an up-to-date account of recent research. On the other hand, the main structural results have been known for some time, and the emphasis there is on a presentation accessible to newcomers to the subject. The intended audience is graduate students in algebra, and researchers in algebra, combinatorics and invariant theory.