Alternative Loop Rings
by Edgar G. Goodaire , Eric Jespers and César Polcino Milies (Eds.)

Persian Title: حلقه حلقه جایگزین

Summary and Info
For the past ten years, alternative loop rings have intrigued mathematicians from a wide crosssection 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 2groups.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 ringtheoretic and grouptheoretic concepts. They present a work which is very much selfcontained. 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.
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