Characterization of Prime Ideals in (Z+,<=D)


  • Sagi Sankar


Poset, Lattice, semi lattice, Convolution, ideal, prime ideal


A convolution is a mapping ô°‚ of the set ô°ˆ + of positive integers into the set ô°† (ô°ˆ + ) of all subsets of ô°ˆ+ such that, for any n ∈ ô°ˆ+ , each member of ô°‚(n) is a divisor of n. If ô°ƒ(n) is the set of all divisors of n, for any n, then ô°ƒ is called the Dirichlet’s convolution. Corresponding to any general convolution ô°‚, we can define a binary relation ≤ô°‚ on ô°ˆ+ by “m ≤ô°‚ n if and only if m ∈ ô°‚(n)â€. It is well known that ô°ˆ+ has the structure of a distributive lattice with respect to the division order. The division ordering is precisely the partial ordering ≤ô°ƒ induced by the Dirichlet’s convolution ô°ƒ. In this paper, we present a characterization for the prime ideals in (ô°ˆ+,≤ô°ƒ) , where ô°ƒ is the Dirichlet’s convolution. 







How to Cite

Characterization of Prime Ideals in (Z+,. (2015). European Journal of Pure and Applied Mathematics, 8(1), 15-25.

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