Groupoids and Smarandache Groupoids

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Definition:Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B in A which is embedded with a stronger structure S.These types of structures occur in our everyday life, that?s why we study them in this book.Thus, as a particular case:A Smarandache Groupoid is a groupoid G which has a proper subset S in G such that S under the operation of G is a semigroup.

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