TY - BOOK
AU - Hazewinkel,Michiel
AU - Gubareni,Nadiya
AU - Kirichenko,V.V.
ED - SpringerLink (Online service)
TI - Algebras, Rings and Modules
T2 - Mathematics and Its Applications
SN - 9781402051418
AV - QA251.5
U1 - 512.46 23
PY - 2007///
CY - Dordrecht
PB - Springer Netherlands
KW - Mathematics
KW - Associative rings
KW - Rings (Algebra)
KW - Category theory (Mathematics)
KW - Homological algebra
KW - Commutative algebra
KW - Commutative rings
KW - Matrix theory
KW - Algebra
KW - Associative Rings and Algebras
KW - Category Theory, Homological Algebra
KW - Commutative Rings and Algebras
KW - Linear and Multilinear Algebras, Matrix Theory
N1 - Groups and group representations -- Quivers and their representations -- Representations of posets and of finite dimensional algebras -- Frobenius algebras and quasi-Frobenius rings -- Right serial rings -- Tiled orders over discrete valuation rings -- Gorenstein matrices
N2 - As a natural continuation of the first volume of Algebras, Rings and Modules, this book provides both the classical aspects of the theory of groups and their representations as well as a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras. Detailed attention is given to special classes of algebras and rings including Frobenius, quasi-Frobenius, right serial rings and tiled orders using the technique of quivers. The most important recent developments in the theory of these rings are examined. The Cartan Determinant Conjecture and some properties of global dimensions of different classes of rings are also given. The last chapters of this volume provide the theory of semiprime Noetherian semiperfect and semidistributive rings. Of course, this book is mainly aimed at researchers in the theory of rings and algebras but graduate and postgraduate students, especially those using algebraic techniques, should also find this book of interest
UR - http://dx.doi.org/10.1007/978-1-4020-5141-8
ER -