TITLE:
Levely Multiplicative Functions on N
AUTHORS:
Salahddeen Khalifa, Moamar Alamari
KEYWORDS:
Prime-Power Decomposition, Levels of, Upward Closed Set, Levely Multiplicative Function
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.15 No.9,
September
25,
2025
ABSTRACT: 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
→
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∈N
and maintains divisibility properties.