Algebras, Rings and Modules

Non-Commutative Algebras and Rings
1. Auflage 2016
ISBN: 978-1-4822-4503-5
Verlag: CRC Press

Buch, Englisch, 388 Seiten, Format (B × H): 157 mm x 234 mm, Gewicht: 703 g

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This volume is a continuation and an in-depth study, stressing the non-commutative nature of the first two volumes of Algebras, Rings and Modules by M. Hazewinkel, N. Gubareni, and V. V. Kirichenko. It is largely independent of the other volumes. The relevant constructions and results from earlier volumes have been presented in this volume.

Autoren/Hrsg.

Hazewinkel, Michiel

Gubareni, Nadiya M

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Preface. Preliminaries. Basic general constructions of rings and modules. Homological dimensions of rings and modules. Goldie and Krull dimensions of rings and modules. Rings with Finiteness conditions. Krull-Remak-Schmidt-Azumaya theorem. Hereditary and semihereditary rings. Serial nonsingular rings. Jacobson's conjecture. Rings related to Finite posets. Distributive and semidistributive rings. The group of extensions. Modules over semiperfect rings. Representations of primitive posets. Representations of quivers, species and finite dimensional algebras. Artinian rings of finite representation type. Semiperfect rings of bounded representation type.

Über Autor(innen)

Michiel Hazewinkel, Nadiya M. Gubareni