arXiv subjects

Ki-Bong Nam

Publications and source records attributed to Ki-Bong Nam.

6 recordsLinked to original sources

arXiv2023

A Note on Finite Number Rings

We define the finite number ring ${\Bbb Z}_n [\sqrt [m] r]$ where $m,n$ are positive integers and $r$ in an integer akin to the definition of the Gaussian integer ${\Bbb Z}[i]$. This idea is also introduced briefly in [7]. By definition, this finite number ring ${\Bbb Z}_n [\sqrt [m] r]$ is naturally isomorphic to the ring ${\Bbb Z}_n[x]/{\langle x^m-r \rangle}$. From an educational standpoint, this description offers a straightforward and elementary presentation of this finite ring, making it suitable for readers who do not have extensive exposure to abstract algebra. We discuss various arithmetical properties of this ring. In particular, when $n=p$ is a prime number and $\mathbb{Z}_p$ contains a primitive $m$-root of unity, we describe the structure of $\mathbb{Z}_n[\sqrt[m]{r}]$ explicitly.

math.RA↗

arXiv2022

P-class is a proper subclass of NP-class; and more

We may give rise to some questions related to the mathematical structures of $P$-class and $NP$-class. We have seen that one is a proper subclass of the other. Here we disclose more that $P$- class turns out to be the proper distributive sublattice of the $NP$- class.

cs.CC↗

arXiv2021

New Gelfond-Type Transcendental Numbers

It is well known that value at a non-zero algebraic number of each of the functions $e^{x}, \ln x, \sin x, \cos x, \tan x, \csc x, \sec x, \cot x, \sinh x,$ $ \cosh x,$ $ \tanh x,$ and $\coth x$ is transcendental number (see Theorem 9.11 of \cite{N}). In the work, we show that for any one of the above mentioned functions, $f(x)$, and for a polynomial $g(x)$ with rational coefficients the zero, if any, of the equation $f(x)=g(x)$ is a transcendental number. We also show that if $f(x)$ and $g(x)$ are polynomials with rational coefficients, then a zero of the equation $e^{f(x)}=g(x)$ is a transcendental number. Finally we show that the existence of an abelian group whose non-zero elements are transcendental numbers.

math.NT↗

arXiv1998

The generalized Witt algebras using additive maps

Wawamoto generalized the Witt algebra using Laurent extension of polynomial ring. We construct the generalized Witt algebra $W(g_p,n)$ by using an additive map $g_p$ from a set of integers into a field of characteristic zero where $1\leq p \leq n.$

math.RT↗

arXiv1997

Simple Lie algebras which generalize Witt algebras

We introduce a new class of simple Lie algebras $W(n,m)$ that generalize the Witt algebra by using "exponential" functions, and also a subalgebra $W^*(n,m)$ thereof; and we show each derivation of $W^*(1,0)$ can be written as a sum of an inner derivation and a scalar derivation. The Lie algebra $W(n,m)$ is $Z$-graded and is infinite growth.

math.RT↗

arXiv1997

Generalized W-type and H-type algebras

It is well known that the Poisson Lie algebra is isomorphic to the Hamiltonian Lie algebra. We show that the Poisson Lie algebra can be embedded properly in the special type Lie algebra. We also generalize the Hamiltonian Lie algebra using exponential functions, and we show that these Lie algebras are simple.

math.RT↗