• Bulletin of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.39-44
• /
• 1996

Throughout this paper $Z^p, Q_p$ and C_p$ will denote the ring of p-adic rational integers, the field of p-adic rational numbers and the completion of the algebraic closure of $Q_p$, respectively. Let $v_p$ be the normalized exponential valuation of $C_p$ with $$\mid$p$\mid$_p = p^{-v_p (p)} = p^{-1}$. We set $p^* = p$ for any prime p > 2 $p^* = 4 for p = 2$.

• Communications of the Korean Mathematical Society
• /
• v.22 no.2
• /
• pp.157-161
• /
• 2007

Let G be a p-mixed abelian group with semi-complete torsion subgroup $G_t$ such that G is splitting or is of torsion-free rank one, and let R be a commutative unitary ring of prime characteristic p. It is proved that the group algebras RG and RH are R-isomorphic for any group H if and only if G and H are isomorphic. This isomorphism relationship extends our earlier results in (Southeast Asian Bull. Math., 2002), (Proc. Amer. Math. Soc., 2002) and (Bull. Korean Math. Soc., 2005) as well as completely settles a problem posed by W. May in (Proc. Amer. Math. Soc., 1979).

• Journal of the Korean Mathematical Society
• /
• v.51 no.4
• /
• pp.721-734
• /
• 2014

Let M be a module over a commutative ring R, and let T(M) be its set of torsion elements. The total torsion element graph of M over R is the graph $T({\Gamma}(M))$ with vertices all elements of M, and two distinct vertices m and n are adjacent if and only if $m+n{\in}T(M)$. In this paper, we study the basic properties and possible structures of two (induced) subgraphs $Tor_0({\Gamma}(M))$ and $T_0({\Gamma}(M))$ of $T({\Gamma}(M))$, with vertices $T(M){\backslash}\{0\}$ and $M{\backslash}\{0\}$, respectively. The main purpose of this paper is to extend the definitions and some results given in [6] to a more general total torsion element graph case.

• Journal of applied mathematics & informatics
• /
• v.16 no.1_2
• /
• pp.251-263
• /
• 2004

In this paper, algorithms for computing the minimal polynomial and the common minimal polynomial of resultant matrices over any field are presented by means of the approach for the Grobner basis of the ideal in the polynomial ring, respectively, and two algorithms for finding the inverses of such matrices are also presented. Finally, an algorithm for the inverse of partitioned matrix with resultant blocks over any field is given, which can be realized by CoCoA 4.0, an algebraic system over the field of rational numbers or the field of residue classes of modulo prime number. We get examples showing the effectiveness of the algorithms.

• Korean Journal of Mathematics
• /
• v.18 no.2
• /
• pp.185-193
• /
• 2010

Let D be an integral domain, and let ${\bar{D}}$ be the integral closure of D. We show that if D is an almost pseudo-valuation domain (APVD), then D is a quasi-$Pr{\ddot{u}}fer$ domain if and only if D=P is a quasi-$Pr{\ddot{u}}fer$ domain for each prime ideal P of D, if and only if ${\bar{D}}$ is a valuation domain. We also show that D(X), the Nagata ring of D, is a locally APVD if and only if D is a locally APVD and ${\bar{D}}$ is a $Pr{\ddot{u}}fer$ domain.

• Journal of the Chungcheong Mathematical Society
• /
• v.7 no.1
• /
• pp.165-182
• /
• 1994

The aim of this paper is to give the partial answer of Vukman's conjecture [2]. From the partial answer we also generalize a classical result of Posner. We prove the following result: Let R be a prime ring with char$(R){\neq}2,3$, and 5. Suppose there exists a nonzero derivation $D:R{\rightarrow}R$ such that the mapping $x{\longmapsto}$ [[[Dx,x],x],x] is centralizing on R. Then R is commutative. Using this result and some results of Sinclair and Johnson, we generalize Yood's noncom-mutative extension of the Singer-Wermer theorem.

• Journal of the Chungcheong Mathematical Society
• /
• v.7 no.1
• /
• pp.117-122
• /
• 1994

In this paper we show that if {$H_n$} is a continuous strong higher derivation of order n on an ultraprime Banach algebra with a constant c, then $c||H_1||^2{\leq}4||H_2||$ and for each $1{\leq}l$ < n $$c^2||H_1||\;||H_{n-l}{\leq}6||H_n||+\frac{3}{2}\sum_{\array{i+j+k=n\\i,j,k{\geq}1}}||H_i||\;||H_j||\;||H_k||+\frac{3}{2}\sum_{\array{i+k=n\\i{\neq}l,\;n-1}}||H_i||\;||H_k|| $$ and for a strong higher derivation {$H_n$} of order n on a prime ring A we also show that if [$H_n$(x),x]=0 for all $x{\in}A$ and for every $n{\geq}1$, then A is commutative or $H_n=0$ for every $n{\geq}1$.

• Honam Mathematical Journal
• /
• v.27 no.3
• /
• pp.399-404
• /
• 2005

Let M be a finite commutative nilpotent algebra over a perfect field k of prime characteristic p and let $M^p$ be the sub-algebra of M generated by $x^p$, $x{\in}M$. Eggert[3] conjectures that $dim_kM{\geq}pdim_kM^p$. In this paper, we show that the conjecture holds for $M=R^+/I$, where $R=k[X_1,\;X_2,\;{\cdots},\;X_t]$ is a polynomial ring with indeterminates $X_1,\;X_2,\;{\cdots},\;X_t$ over k and $R^+$ is the maximal ideal of R generated by $X_1,\;X_2,{\cdots},\;X_t$ and I is a monomial ideal of R containing $X_1^{n_1+1},\;X_2^{n_2+1},\;{\cdots},\;X_t^{n_t+1}$ ($n_i{\geq}0$ for all i).

• Proceedings of the KIEE Conference
• /
• 1998.11a
• /
• pp.103-105
• /
• 1998

This paper presents the compensated 2-D magnetic fields analysis of superconducting AC generator(SCG) by using efficient 2-D model. 3-D analysis is necessary for the accurate analysis because SCG has a large leakage flux owing to the air cored winding and end ring structure. However, in 3-D FEM, considering the movement of rotor is difficult, so efficient 2-D model which can compensate the leakage flux has been proposed and the movement of rotor is easily considered. The characteristics in transient state of SCG and the prime role of damper also have been evaluated.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.6
• /
• pp.1385-1422
• /
• 2019

Let p be an odd prime. The algebraic structure of all negacyclic codes of length $8_{p^s}$ over the finite commutative chain ring ${\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m}$ where $u^2=0$ is studied in this paper. Moreover, we classify all negacyclic codes of length $8_{p^s}$ over ${\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m}$ into 5 cases, i.e., $p^m{\equiv}1$ (mod 16), $p^m{\equiv}3$, 11 (mod 16), $p^m{\equiv}5$, 13 (mod 16), $p^m{\equiv}7$, 15 (mod 16) and $p^m{\equiv}9$ (mod 16). From that, the structures of dual and some self-dual negacyclic codes and number of codewords of negacyclic codes are obtained.