Topics on multiplicative groups of finite commutative rings
Units of Finite Rings
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This text contains a concise collection of papers published in international journals and work given at mathematics conferences and seminars. It is assumed that the reader is familiar with the knowledge of the concepts of group theory and ring theory offered in undergraduate courses in modern algebra. The main objective of this text is to bring to a wider research audience a readable and rigorous account of a certain type of finite rings and solve some concrete algebraic problems of determining the structure of their groups of units. The book is divided into two parts. The first is concerned w...
This text contains a concise collection of papers published in international journals and work given at mathematics conferences and seminars. It is assumed that the reader is familiar with the knowledge of the concepts of group theory and ring theory offered in undergraduate courses in modern algebra. The main objective of this text is to bring to a wider research audience a readable and rigorous account of a certain type of finite rings and solve some concrete algebraic problems of determining the structure of their groups of units. The book is divided into two parts. The first is concerned with defining concepts and terminology, assembling elementary facts and developing the theory of completely primary finite rings. The second, and the most important part, concerns the problem of determining the structure of the group of units of these rings. Graduate students wishing to acquire some knowledge of finite ring theory and structure of their groups of units will find this an excellent text for self-study.
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