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Module theory is an important tool for many different branches of mathematics, as well as being an interesting subject in its own right. Within module theory, the concept of injective modules is particularly important. Extending modules form a natural class of modules which is more general than the class of injective modules but retains many of its desirable properties. This book gathers together for the first time in one place recent work on extending modules. It is aimed at anyone with a basic knowledge of ring and module theory.
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The International Conference on Algebra and its Applications held in Athens, Ohio, June 18-21, 2008 and sponsored by the Ohio University Center for Ring TheoryanditsApplications(CRA)hadasitscentralpurposetohonorSurenderK. Jain, the Center's retiring ?rst director, on the dual occasion of his 70th birthday and of his retirement from Ohio University. With this volume we celebrate the contributions to Algebra of our distinguished colleague. One of Surender's main attributes has been the way in which he radiates enthusiasm about mathematical research; his eagerness to pursue mathematical problems is contagious; we hope that reading this excellent collection of scholarly writings will have a similar e?ect onourreadersandthatyouwillbeinspiredtocontinuethepursuitofRingTheory as well as Algebra and its Applications. As with previous installments of CRA conferences, the underlying principle behind the meeting was to bring together specialists on the various areas of - gebra in order to promote communication and cross pollination between them. In particular, a common philosophy of our conferences through the years has been to bringalgebraistswho focus onthe theoreticalaspects ofour?eld withthose others who embraceapplicationsofAlgebraindiverseareas.Clearly,asa re?ectionofthe interests of the organizers,the applications we emphasized were largely within the realmofCoding Theory.The philosophybehind the organizationofthe conference has undoubtedly impacted this Proceedings volume. For the most part, the contributors delivered related talks at the conference itself.However,therearealsoacoupleofcontributionsinthisvolumefromauthors who could not be present at the conference but wanted to participate and honor Dr. Jain on this occasion. All papers were subject to a strict process of refereeing and, in fact, not all submissions were accepted for publication.