| Abstract |
The history of nonassociative algebraic structures can be traced at least to the middle of the 19th century. Today, the theory of nonassociative algebraic structures is an enormously broad and greatly advanced area. Interesting new algebraic ideas arise, with challenging opportunities to discover connections to other areas of mathematics, natural sciences and engineering. On the other hand, computer-assisted methods proved useful in the development of the theory of nonassociative algebraic structures, in particulary in finding proofs and constructing examples. We will try to present a brief overview of the origins of nonassociative algebraic structures, selection of current research topics and future directions, generalizations within the framework of classical, fuzzy and intuitionistic logic, and further applications. Topics include, but are not limited, to:
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