Journal Name:
- European Journal of Pure and Applied Mathematics
Key Words:
Author Name | University of Author |
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Abstract (2. Language):
A convolution is a mapping C of the set Z+ of positive integers into the set P (Z+) of all
subsets of Z+ such that, for any n ∈ Z+ , each member of C(n) is a divisor of n. If D(n) is the set of
all divisors of n, for any n, then D is called the Dirichlet’s convolution. Corresponding to any general
convolution C, we can define a binary relation ≤C on Z+ by “m ≤C n if and only if m ∈ C(n)”.
It is well known that Z+ has the structure of a distributive lattice with respect to the division order.
The division ordering is precisely the partial ordering ≤D induced by the Dirichlet’s convolution D. In
this paper, we present a characterization for the prime ideals in (Z+,≤D) , where D is the Dirichlet’s
convolution.
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