Characterization of Prime Ideals in (Z+,<=D)
Sagi Sankar · European Journal of Pure and Applied Mathematics · 2015
A convolution is a mapping of the set + of positive integers into the set ( + ) of all subsets of + such that, for any n ∈ + , each member of (n) is a divisor of n. If (n) is the set of all divisors of n, for any n, then is called the Dirichlet’s convolution. Corresponding to any general convolution , we can define a binary relation ≤ on + by “m ≤ n if and only if m ∈ (n)”. It is well known that + has the structure of a distributive lattice with respect to the division order. The division ordering is precisely the partial ordering ≤ induced by the Dirichlet’s convolution . In this paper, we present a characterization for the prime ideals in (+,≤) , where is the Dirichlet’s convolution.