Background
Karpilovsky, Gregory was born on December 5, 1940 in Kiev, Ukraine. Son of Ilia Aronovich and Roza Gershevna (Kaptournik) Karpilovsky.
(In the past 15 years, the theory of crossed products has ...)
In the past 15 years, the theory of crossed products has enjoyed a period of vigorous development. The foundations have been strengthened and reorganized from new points of view, especially from the viewpoint of graded rings. The purpose of this monograph is to give, in a self-contained manner, an up-to-date account of various aspects of this development, in an effort to convey a comprehensive picture of the current state of the subject. It is assumed that the reader has had the equivalent of a standard first-year graduate course, thus familiarity with basic ring-theoretic and group-theoretic concepts and an understanding of elementary properties of modules, tensor products and fields. A chapter on algebraic preliminaries is included, which briefly surveys topics required later in the book.
http://www.amazon.com/gp/product/0444556966/?tag=2022091-20
(The purpose of this book is to give a self-contained, up-...)
The purpose of this book is to give a self-contained, up-to-date account of the structure of unit groups of classical rings. In so doing, the work draws together four areas of mathematics: ring theory, group theory, group representation theory, and algebraic number theory. The ensuing interplay between these disciplines provides a unique source of enrichment for each of them. The main theme centers on two related problems: to determine the isomorphism class of the unit group (U)R of ring R in terms of natural invariants associated with R; and to find an effective method for the construction of units of ring R. Various threads of the development are tied together to convey a comprehensive picture of the current state of the subject. Examples are provided to help research workers who need to compute explicitly unit groups of certain rings. A familiarity with basic ring-theoretic and group-theoretic concepts is assumed, but a chapter on algebraic preliminaries is included. The text is distinguished by its very clear exposition.
http://www.amazon.com/gp/product/0198535570/?tag=2022091-20
(Let G be a finite group and let F be a field. It is well ...)
Let G be a finite group and let F be a field. It is well known that linear representations of G over F can be interpreted as modules over the group algebra FG. Thus the investigation of ring-theoretic structure of the Jacobson radical J (FG) of FG is of fundamental importance. During the last two decades the subject has been pursued by a number of researchers and many interesting results have been obtained. This volume examines these results. The main body of the theory is presented, giving the central ideas, the basic results and the fundamental methods. It is assumed that the reader has had the equivalent of a standard first-year graduate algebra course, thus familiarity with basic ring-theoretic and group-theoretic concepts and an understanding of elementary properties of modules, tensor products and fields. A chapter on algebraic preliminaries is included, providing a survey of topics needed later in the book. There is a fairly large bibliography of works which are either directly relevant to the text or offer supplementary material of interest.
http://www.amazon.com/gp/product/0444556893/?tag=2022091-20
educator mathematician researcher
Karpilovsky, Gregory was born on December 5, 1940 in Kiev, Ukraine. Son of Ilia Aronovich and Roza Gershevna (Kaptournik) Karpilovsky.
Bachelor of Science with honors, University Uzhgorod, Ukraine, 1966. Doctor of Philosophy, Institute Radio-electronics, Kharkov, Ukraine, 1970.
Assistant professor Military Academy, Kiev, Russia, 1969—1970. Senior lecturer Technology Institute, Astrakhan, Russia, 1971—1972. Assistant professor Agricultural Academy, Kiev, 1972—1973.
Tutor University New South Wales, Sydney, 1974—1977. Lecturer La Trobe University, Melbourne, Australia, 1978—1983. Professor mathematics University Witwatersrand, Johannesburg, since 1984.
Reviewer professional journals, since 1974.
(The purpose of this book is to give a self-contained, up-...)
(In the past 15 years, the theory of crossed products has ...)
(Let G be a finite group and let F be a field. It is well ...)
Fellow: International Biographical Association. Member: confederation Chivalry, American Mathematics Society, Australian Mathematics Society.
Married Helen Swiatlo Karpilovsky, June 27, 1976. Children: Suzanne, Elliott Michael.