Algebraic Structures Using Subsets
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Algebraic Structures Using Subsets
Author: W. B. Vasantha Kandasamy, Florentin Smarandache
language: en
Publisher: Infinite Study
Release Date: 2012
"[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."--
Algebraic Structures Using Subsets
"[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."--