Themes in Torsion Theory : Relatively Max, Injective and Extending (CS) modules

ISBN-13: 9783639157826 / Angielski / Miękka / 2009 / 140 str.

Stelios Charalambides

Opis

The purpose of this book is to generalize to thetorsion-theoretic setting various concepts andresults from the theory of rings and modules. Inparticular we work in the areas of chain conditionson modules, injectivity and CS (extending) modules.At the outset we acquaint the reader with the mainideas used in torsion theory. We then obtain resultsthat fall into three more or less interrelated areas.In the first area we introduce a torsion-theoreticanalogue of Max modules and generalize an importantcharacterization of Noetherian rings by Shock. Thesecond area deals with various flavors of relativeinjectivity. We generalize well-known results byFuchs, Azumaya, Faith, Albu and Nastasescu andCailleau. In the third area we introduce a couple ofnew concepts with the aim of bringing to thetorsion-theoretic setting the concept of a CS orextending module. Our motivation is to provide atorsion-theoretic analogue of a celebrated result byOkado.This book should appeal to researchers in the theoryof rings and modules with particular emphasis ontorsion theory.

O autorze

Stelios A. Charalambides, BSc, MSc, PhD.
Studied Mathematics (Ring Theory) at Winnipeg, Simon Fraser and
Otago Universities.
Earned several scholarships including two form the Commonwealth.
Held various teaching and research positions in Canada, Cyprus,
New Zealand, USA and Norway.
Currently a Research Fellow at Cyprus University of Technology.