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Full-Text Articles in Analysis
Algebraic Structures Using [0,N), Florentin Smarandache, Vasantha Kandasamy
Algebraic Structures Using [0,N), Florentin Smarandache, Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time introduce a new method of building algebraic structures on the interval [0, n). This study is interesting and innovative. However, [0, n) is a semigroup under product, × modulo n and a semigroup under min or max operation. Further [0, n) is a group under addition modulo n. We see [0, n) under both max and min operation is a semiring. [0, n) under + and × is not in general a ring. We define S = {[0, n), +, ×} to be a pseudo special ring as the distributive law is …
Algebraic Structures Using Subsets, Florentin Smarandache, W.B Vasantha Kandasamy
Algebraic Structures Using Subsets, Florentin Smarandache, W.B Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
The study of subsets and giving algebraic structure to these subsets of a set started in the mid 18th century by George Boole. The first systematic presentation of Boolean algebra emerged in 1860s in papers written by William Jevons and Charles Sanders Peirce. Thus we see if P(X) denotes the collection of all subsets of the set X, then P(X) under the op erations of union and intersection is a Boolean algebra. Next the subsets of a set was used in the construction of topological spaces. We in this book consider subsets of a semigroup or a group or a …