Download or read book Algebraic Structures Using Subsets written by W. B. Vasantha Kandasamy, Florentin Smarandache and published by Infinite Study. This book was released on 2012 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: "[The] study of algebraic structures using subsets [was] started by George Boole. After the invention of Boolean algebra, subsets are not used in building any algebraic structures. In this book we develop algebraic structures using subsets of a set or a group, or a semiring, or a ring, and get algebraic structures. Using group or semigroup, we only get subset semigroups. Using ring or semiring, we get only subset semirings. By this method, we get [an] infinite number of non-commutative semirings of finite order. We build subset semivector spaces, [and] describe and develop several interesting properties about them."--