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Full-Text Articles in Number Theory
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 …
Interval Algebraic Bistructures, Florentin Smarandache, W.B. Vasantha Kandasamy
Interval Algebraic Bistructures, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
Authors in this book construct interval bistructures using only interval groups, interval loops, interval semigroups and interval groupoids. Several results enjoyed by these interval bistructures are described. By this method, we obtain interval bistructures which are associative or non associative or quasi associative. The term quasi is used mainly in the interval bistructure B = B1 ∪ B2 (or in n-interval structure) if one of B1 (or B2) enjoys an algebraic property and the other does not enjoy that property (one section of interval structure satisfies an algebraic property and the remaining section does not satisfy that particular property). The …