|
Showing 1 - 6 of
6 matches in All Departments
A classic text and standard reference for a generation, this volume
and its companion are the work of an expert algebraist who taught
at Yale for two decades. Nathan Jacobson's books possess a
conceptual and theoretical orientation, and in addition to their
value as classroom texts, they serve as valuable references.
Volume I explores all of the topics typically covered in
undergraduate courses, including the rudiments of set theory, group
theory, rings, modules, Galois theory, polynomials, linear algebra,
and associative algebra. Its comprehensive treatment extends to
such rigorous topics as Lie and Jordan algebras, lattices, and
Boolean algebras. Exercises appear throughout the text, along with
insightful, carefully explained proofs. Volume II comprises all
subjects customary to a first-year graduate course in algebra, and
it revisits many topics from Volume I with greater depth and
sophistication.
A classic text and standard reference for a generation, this volume
and its companion are the work of an expert algebraist who taught
at Yale for more than three decades. Nathan Jacobson's books
possess a conceptual and theoretical orientation; in addition to
their value as classroom texts, they serve as valuable
references.
Volume II comprises all of the subjects usually covered in a
first-year graduate course in algebra. Topics include categories,
universal algebra, modules, basic structure theory of rings,
classical representation theory of finite groups, elements of
homological algebra with applications, commutative ideal theory,
and formally real fields. In addition to the immediate introduction
and constant use of categories and functors, it revisits many
topics from Volume I with greater depth and sophistication.
Exercises appear throughout the text, along with insightful,
carefully explained proofs.
Here, the eminent algebraist, Nathan Jacobsen, concentrates on
those algebras that have an involution. Although they appear in
many contexts, these algebras first arose in the study of the
so-called "multiplication algebras of Riemann matrices". Of
particular interest are the Jordan algebras determined by such
algebras, and thus their structure is discussed in detail. Two
important concepts also dealt with are the universal enveloping
algebras and the reduced norm. However, the largest part of the
book is the fifth chapter, which focuses on involutorial simple
algebras of finite dimension over a field.
Emmy Noether (1882-1935) was one of the most influential
mathematicians of the 20th century. The development of abstract
algebra, which is one of the most distinctive innovations of 20th
century mathematics, can largely be traced back to her - in her
published papers, lectures and her personal influence on her
contemporaries. By now her contributions have become so thoroughly
absorbed into our mathematical culture that only rarely are they
specifically attributed to her. This book presents an extensive
collection of her work. Albert Einstein wrote in a letter to the
New York Times of May 1st, 1935: "In the judgment of the most
competent living mathematicians, Fraulein Noether was the most
significant creative mathematical genius thus far produced since
the higher education of women began. In the realm of algebra, in
which the most gifted mathematicians have been busy for centuries,
she discovered methods which have proved of enormous importance in
the development of the present-day younger generation of
mathematicians." Emmy Noether leistete grundlegende Arbeiten zur
Abstrakten Algebra. Ihre Auffassung von Mathematik war sehr
nutzlich fur die damalige Physik, aber wurde auch kontrovers
diskutiert. Die Debatte ging darum, ob Mathematik eher konzeptuell
und abstract (intuitionistisch) oder mehr physikalisch basiert und
angewandt (konstruktionistisch) sein sollte. Noethers konzeptuelle
Auffassung der Algebra fuhrte zu neuen Grundlagen, die Algebra,
Geometrie, Lineare Algebra, Topologie und Logik vereinheitlichten."
Here, the eminent algebraist, Nathan Jacobsen, concentrates on those algebras that have an involution. Although they appear in many contexts, these algebras first arose in the study of the so-called "multiplication algebras of Riemann matrices". Of particular interest are the Jordan algebras determined by such algebras, and thus their structure is discussed in detail. Two important concepts also dealt with are the universal enveloping algebras and the reduced norm. However, the largest part of the book is the fifth chapter, which focuses on involutorial simple algebras of finite dimension over a field.
This book contains the collected works of A. Adrian Albert, a
leading algebraist of the twentieth century. Albert made many
important contributions to the theory of the Brauer group and
central simple algebras, Riemann matrices, nonassociative algebras,
and other topics. Part 1 focuses on associative algebras and
Riemann matrices, and Part 2 on nonassociative algebras and
miscellany. Because much of Albert's work remains of vital interest
in contemporary research, this volume will interest mathematicians
in a variety of areas.
|
|