ABSTRACT
This chapter discusses knots, their planar diagrams and the semi group structure on knots; the latter is isomorphic to that on natural numbers with respect to multiplication. It investigates knot arithmetics and to establish some properties of multiplication and decomposition of knots. The existence of non– invertible knots had been an open problem. This problem was solved positively in 1964 by H. F. Trotter. The semi group of knot isotopy classes with respect to concatenation is isomorphic to the semi group of natural numbers with respect to multiplication. Prime knots correspond to prime numbers. The polygonal knot planar diagram is defined analogously to the smooth diagram. The semigroup of knot isotopy classes with respect to concatenation is isomorphic to the semigroup of natural numbers with respect to multiplication. Prime knots correspond to prime numbers. Each knot can be decomposed in no more than a finite number of prime knots.
