Author(s)

Salahddeen Khalifa¹, Moamar Alamari²

¹Mathematicl Department, Faculty of Science, Gharyan University, Gharyan, Libya.
²Higher Institute of Engineering Technology, Zliten, Libya.

In this paper, as a result of dividing the set of natural numbers into disjoint levels, we have studied levely multiplicative functions that are defined from $N$ to $N$ and which keep numbers at the same level when restricted on levels, i.e. $f_{|}{}_{L_i}:L_i\to L_i$ . We have defined the level multiplicative function and explained how to generate it using the restriction function $f_{|}{}_{L_1}$ . Furthermore, if $f_{|}{}_{L_1}$ is bijective, then all $f_{|}{}_{L_i}$ and $f$ are bijective functions. Moreover, the levely multiplicative function preserves the unique factorization for any number $n\in N$ and maintains divisibility properties.

Prime-Power Decomposition, Levels of , Upward Closed Set, Levely Multiplicative Function

Khalifa, S. and Alamari, M. (2025) Levely Multiplicative Functions on N. Advances in Pure Mathematics, 15, 643-650. doi: 10.4236/apm.2025.159033.