@article{Characterization of Prime Ideals in (Z+,_2015, place={Maryland, USA}, volume={8}, url={https://www.ejpam.com/index.php/ejpam/article/view/1878}, abstractNote={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 âˆˆ 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 Dirichletâ€™s convolution. Corresponding to any general convolution ô°‚, we can define a binary relation â‰¤ô°‚ on ô°ˆ+ by â€œm â‰¤ô°‚ n if and only if m âˆˆ 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 â‰¤ô°ƒ induced by the Dirichletâ€™s convolution ô°ƒ. In this paper, we present a characterization for the prime ideals in (ô°ˆ+,â‰¤ô°ƒ) , where ô°ƒ is the Dirichletâ€™s convolution.Â }, number={1}, journal={European Journal of Pure and Applied Mathematics}, year={2015}, month={Jan.}, pages={15–25} }