W. B. Vasantha Kandasamy, Florentin Smarandache
2014
Study of algebraic structures built using [0, n) happens to be one of an interesting and innovative research. Here in this book authors define non associative algebraic structures using the interval [0, n). Here the authors define two types of groupoids using [0, n) both of them are of infinite order. It is an open conjecture to find whether these new class of groupoids satisfy any of the special identities like Moufang identity or Bol identity or Bruck identity or so on. We know on [0, n) we cannot build rings only pseudo rings, however in this book the authors use these type I and type II groupoids to build non associative rings and semirings. Several interesting results are derived and some open problems are suggested.
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