Rings, Groups, and Algebras

ISBN-13: 9781138401990 / Angielski / Twarda / 2017

X. Cao

Opis

Integrates and summarizes the significant developments made by Chinese mathematicians in rings, groups, and algebras since the 1950s. This work examines topics in Hopf algebra, representation theory, semigroups, finite groups, homology algebra, module theory and valuation theory.

Spis treści

Preface -- Contributors -- Structure of Finite Groups /CHEN Zhongmu, SHI Wujie, and CHEN Guiyun -- The Representation and Cohomology Theory of Modular Lie Algebras /CHIU Sen -- Valuation Theory and Generalizations of Hilbert's 17th Problem /DAI Zhizhong and ZENG Guangxing -- Modules over Hyperfinite Groups /DUANZ. Y. -- Pointed Groups and Nilpotent Blocks /FAN Yun -- Near-Rings in China: Past and Present /FONG Yuen -- The Theory of Formations /GUO Wenbin -- Some Recent Developments in Filtered Ring and Graded Ring Theory in China /LI Huishi -- Representation Theory of Finite-Dimensional Algebras in China /LIU Shaoxue and ZHANG Pu -- On Regular Semigroups and Their Generalizations /SHUM Karping and GUO Yuqi -- Primitive Rings, Infinite Matrix Rings, and Morita-like Equivalences /SHUM Karping and XU Y onghua -- On Maximal Subgroups of Finite Groups /WANG Yamin -- Recent Developments in Morita Duality /XUE Weimin -- Some Results on Homological Algebra and Module Theory /ZHOU Boxun and TONG Wenting -- Some Progress in Algebric K-Theory in China /ZHOU Boxun and TONG Wenting.

O autorze

X. H. CAO is a Professor of Mathematics at the East China Normal University, Shanghai, People's Republic of China. He received the Ph.D. degree (I 950) from the University of Michigan, Ann Arbor. S. X. Liu is a Professor of Mathematics and former Chairman of the Institute of Mathematics at Beijing Normal University, People's Republic of China. He received the Ph.D. degree (1956) in mathematics from Moscow M. V. Lomonosov State University, Russia. K. P. SHUM is a Senior Lecturer in mathematics at the Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, and a former President of the Southeast Asian Mathe­matical Society. He received the Ph.D. degree (1971) in mathematics from the University of Alberta, Edmonton, Canada. C. C. YANG is a Professor ofMathematics at the Hong Kong University of Science and Tech­nology, Clear Water Bay, Kowloon, Hong Kong. He received the Ph.D. degree (1979) in mathematics from the University of Wisconsin-Madison.