Advances in Ring Theory: (Trends in Mathematics)

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.

Table of Contents:
Applications of Cogalois Theory to Elementary Field Arithmetic.- On Big Lattices of Classes of R-modules Defined by Closure Properties.- Reversible and Duo Group Rings.- Principally Quasi-Baer Ring Hulls.- Strongly Prime Ideals of Near-rings of Continuous Functions.- Elements of Minimal Prime Ideals in General Rings.- On a Theorem of Camps and Dicks.- Applications of the Stone Duality in the Theory of Precompact Boolean Rings.- Over Rings and Functors.- On Some Classes of Repeated-root Constacyclic Codes of Length a Power of 2 over Galois Rings.- Couniformly Presented Modules and Dualities.- Semiclassical Limits of Quantized Coordinate Rings.- On Unit-Central Rings.- Symplectic Modules and von Neumann Regular Matrices over Commutative Rings.- Extensions of Simple Modules and the Converse of Schur’s Lemma.- Report on Exchange Rings.- Filtrations in Semisimple Lie Algebras, III.- On the Blowing-up Rings, Arf Rings and Type Sequences.- A Guide to Supertropical Algebra.- Projective Modules, Idempotent Ideals and Intersection Theorems.- On Ef-extending Modules and Rings with Chain Conditions.- On Clean Group Rings.