Lattice Structures on Z+ Induced by Convolutions
Keywords:Poset, Lattice, Support, Convolution, Multiplicative, Relatively Prime.
AbstractA Convolution C is a mapping of the set Z+ of positive integers into the power set P(Z+) such that every member of C(n) is a divisor of n. If for any n, D(n) is the set of all positive divisors of n , then D is called the Dirichletâ€™s convolution. It is well known that Z+ has the structure of a distributive lattice with respect to the division order. Corresponding to any general convolution C,
one can define a binary relation â‰¤C on Z+ by â€˜ m â‰¤C n if and only if m âˆˆ C(n)â€™ . In this paper we characterize Convolutions C which induce partial orders with respect to which Z+ has the structure of a semi lattice or lattice and various lattice theoretic properties are discussed in terms of convolution.
How to Cite
Swamy, U., & Sankar, S. (2011). Lattice Structures on Z+ Induced by Convolutions. European Journal of Pure and Applied Mathematics, 4(4), 424–434. Retrieved from https://www.ejpam.com/index.php/ejpam/article/view/1373
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