The authors in this book construct a large class of finite subset groupoids as well as a large class of infinite subset groupoids. Here the conditions under which these subset groupoids satisfy special identities like Bol Identity, Moufang Identity, right alternative identity and so on are found.
In fact, it is an open problem to find subset groupoids to satisfy special identities, even if the groupoid over which they are defined do not satisfy the special identities.
In this book the authors introduce the new notions of subset polynomial semirings and subset matrix semirings. Solving subset polynomial equations is an interesting exercise.
Open problems about the solution set of subset polynomials are proposed.