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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 grou

Alternative rings --- Group rings --- Loops (Group theory) --- 512.55 --- 512.55 Rings and modules --- Rings and modules --- Group theory --- Rings (Algebra) --- Loop groups --- Nonassociative rings --- Alternative rings. --- Group rings.