For the past ten years, alternative loop rings have intrigued mathematicians from a wide cross-section of modern algebra. As a consequence, the theory of alternative loop rings has grown tremendously.One of the main developments is the complete characterization of loops which have an alternative but not associative, loop ring. Furthermore, there is a very close relationship between the algebraic structures of loop rings and of group rings over 2-groups.Another major topic of research is the study of the unit loop of the integral loop ring. Here the interaction between loop rings and group rings is of immense interest.This is the first survey of the theory of alternative loop rings and related issues. Due to the strong interaction between loop rings and certain group rings, many results on group rings have been included, some of which are published for the first time. The authors often provide a new viewpoint and novel, elementary proofs in cases where results are already known.The authors assume only that the reader is familiar with basic ring-theoretic and group-theoretic concepts. They present a work which is very much self-contained. It is thus a valuable reference to the student as well as the research mathematician. An extensive bibliography of references which are either directly relevant to the text or which offer supplementary material of interest, are also included.

For the past ten years, alternative loop rings have intrigued mathematicians from a wide cross-section of modern algebra. As a consequence, the theory of alternative loop rings has grown tremendously. One of the main developments is the complete characterization of loops which have an alternative but not associative, loop ring. Furthermore, there is a very close relationship between the algebraic structures of loop rings and of group rings over 2-groups. Another major topic of research is the study of the unit loop of the integral loop ring. Here the interaction between loop rings and group rings is of immense interest. This is the first survey of the theory of alternative loop rings and related issues. Due to the strong interaction between loop rings and certain group rings, many results on group rings have been included, some of which are published for the first time. The authors often provide a new viewpoint and novel, elementary proofs in cases where results are already known. The authors assume only that the reader is familiar with basic ring-theoretic and group-theoretic concepts. They present a work which is very much self-contained. It is thus a valuable reference to the student as well as the research mathematician. An extensive bibliography of references which are either directly relevant to the text or which offer supplementary material of interest, are also included.

With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences.

This volume contains contributions from the conference on "Algebras, Representations and Applications" (Maresias, Brazil, August 26-September 1, 2007), in honor of Ivan Shestakov's 60th birthday. The collection of papers presented here is of great interest to graduate students and researchers working in the theory of Lie and Jordan algebras and superalgebras and their representations, Hopf algebras, Poisson algebras, Quantum Groups, Group Rings and other topics.

The Indian National. Science Academy has planned to bring out monographs on special topics with the aim of providing acce~sible surveys/reviews of topics of current research in various fields. Prof. S.K. Malik, FNA, Editor of Publications INSA asked me in October 1997 to edit a volume on algebra in this series. I invited a number of algebraists, several of them working in group rings, and it is with great satisfaction and sincere thanks to the authors that I present here in Algebra: Some Recent Advances the sixteen contributions received in response to my invitations. I.B.S. Passi On Abelian Difference Sets K. r Arasu* and Surinder K. Sehgal 1. Introduction We review some existence and nonexistence results - new and old - on abelian difference sets. Recent surveys on difference sets can be found in Arasu (1990), Jungnickel (1992a, b), Pott (1995), Jungnickel and Schmidt (1997), and Davis and Jedwab (1996). Standard references for difference sets are Baumert (1971), Beth et al. (1998), and Lander (1983). This article presents a flavour of the subject, by discussing some selected topics. Difference sets are very important in combinatorial design theory and in commu nication engineering while designing sequences with good correlation properties. Our extended bibliography covers a wide variety of papers written in the area of difference sets and related topics.