• Bulletin of the Korean Mathematical Society
• /
• v.42 no.3
• /
• pp.477-484
• /
• 2005

Let R be a ring with an automorphism 17. An ideal [ of R is ($\sigma$-ideal of R if $\sigma$(I).= I. A proper ideal P of R is ($\sigma$-prime ideal of R if P is a $\sigma$-ideal of R and for $\sigma$-ideals I and J of R, IJ $\subseteq$ P implies that I $\subseteq$ P or J $\subseteq$ P. A proper ideal Q of R is $\sigma$-semiprime ideal of Q if Q is a $\sigma$-ideal and for a $\sigma$-ideal I of R, I$^{2}$ $\subseteq$ Q implies that I $\subseteq$ Q. The $\sigma$-prime radical is defined by the intersection of all $\sigma$-prime ideals of R and is denoted by P$_{(R). In this paper, the following results are obtained: (1) For a principal ideal domain R, P$_{(R) is the smallest $\sigma$-semiprime ideal of R; (2) For any ring R with an automorphism $\sigma$ and for a skew Laurent polynomial ring R[x, x$^{-1}$; $\sigma$], the prime radical of R[x, x$^{-1}$; $\sigma$] is equal to P$_{(R)[x, x$^{-1}$; $\sigma$ ].

• Communications of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.1075-1082
• /
• 2018

Let R be a commutative ring, G be an Abelian group, and let RG be the group ring. We say that RG is a U-group ring if a is a unit in RG if and only if ${\epsilon}(a)$ is a unit in R. We show that RG is a U-group ring if and only if G is a p-group and $p{\in}J(R)$. We give some properties of U-group rings and investigate some properties of well known rings, such as Hermite rings and rings with stable range, in the presence of U-group rings.

• Bulletin of the Korean Mathematical Society
• /
• v.31 no.2
• /
• pp.163-165
• /
• 1994

Modules which satisfy the converse of Schur's lemma have been studied by many authors. In [6], R. Ware proved that a projective module P over a semiprime ring R is irreducible if and only if En $d_{R}$(P) is a division ring. Also, Y. Hirano and J.K. Park proved that a torsionless module M over a semiprime ring R is irreducible if and only if En $d_{R}$(M) is a division ring. In case R is a commutative ring, we obtain the following: An R-module M is irreducible if and only if En $d_{R}$(M) is a division ring and M is a multiplication R-module. Throughout this paper, R is commutative ring with identity and all modules are unital left R-modules. Let R be a commutative ring with identity and let M be an R-module. Then M is called a multiplication module if for each submodule N of M, there exists and ideal I of R such that N=IM. Cyclic R-modules are multiplication modules. In particular, irreducible R-modules are multiplication modules.dules.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.1
• /
• pp.115-137
• /
• 2018

Let $R_{u{^2},v^2,w^2,p}$ be a finite non chain ring ${\mathbb{F}}_p[u,v,w]{\langle}u^2,\;v^2,\;w^2,\;uv-vu,\;vw-wv,\;uw-wu{\rangle}$, where p is a prime number. This ring is a part of family of Frobenius rings. In this paper, we explore the structures of cyclic codes over the ring $R_{u{^2},v^2,w^2,p}$ of arbitrary length. We obtain a unique set of generators for these codes and also characterize free cyclic codes. We show that Gray images of cyclic codes are 8-quasicyclic binary linear codes of length 8n over ${\mathbb{F}}_p$. We also determine the rank and the Hamming distance for these codes. At last, we have given some examples.

• Kyungpook Mathematical Journal
• /
• v.49 no.3
• /
• pp.451-456
• /
• 2009

Let R be a ring. We give some new characterizations of QF under the special annihilators condition. Some known results are obtained as corollaries.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.149-156
• /
• 2001

In this paper, we initiate the investigation of ring in which all the additive endomorphisms are generated by ring endomorphisms (AGE-rings). This study was motivated by the work on the Sullivan’s Research Problem [11]: Characterize those rings in which every additive endomorphism is a ring endomorphism (AE-rings). The purpose of this paper is to obtain a certain characterization of AGE-rings, and investigate some relations between AGE and LSD-generated rings.

• Journal of the Chungcheong Mathematical Society
• /
• v.19 no.3
• /
• pp.245-261
• /
• 2006

In this paper, we prove the generalized Hyers-Ulam stability of ring homomorphisms over the p-adic field $\mathbb{Q}_p$ associated with the Cauchy functional equation f(x+y) = f(x)+f(y) and the Cauchy-Jensen functional equation $2f(\frac{x+y}{2}+z)=f(x)+f(y)+2f(z)$.

• Journal of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.381-401
• /
• 2016

According to Jacobson [31], a right ideal is bounded if it contains a non-zero ideal, and Faith [15] called a ring strongly right bounded if every non-zero right ideal is bounded. From [30], a ring is strongly right AB if every non-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy Property (A) and the conditions asked by Nielsen [42]. It is shown that for a u.p.-monoid M and ${\sigma}:M{\rightarrow}End(R)$ a compatible monoid homomorphism, if R is reversible, then the skew monoid ring R * M is strongly right AB. If R is a strongly right AB ring, M is a u.p.-monoid and ${\sigma}:M{\rightarrow}End(R)$ is a weakly rigid monoid homomorphism, then the skew monoid ring R * M has right Property (A).

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
• /
• v.13 no.5
• /
• pp.371-375
• /
• 2000

In this paper a new conductivity modulated power transistor called the Lateral Insulated Gated Bipolar Transistor which included n+ ring and p-channel gate is presented. A new lateral IGBT structure is proposed to suppress latch-up and to improve turn off time by imploying n+ ring and p-channel gate and verified by MEDICI. The simulated I-V characteristics at $V_{G}$=15V show that the latch up occurs at $V_{A}$=18V and 6.9$\times$10$^{-5}$ A/${\mu}{\textrm}{m}$ for the proposed LIGBT while the conventional LIGBT latches at $V_{A}$=1.3V and 1.96${\mu}{\textrm}{m}$10$^{-5A}$${\mu}{\textrm}{m}$. It is shown that turn off characteristic of new LIGBT is 8 times than that of conventional LIGBT. And noble LIGBT is not n+ buffer layer because that It includes p channel gate and n+ ring. Therefore Mask for the buffer layer isn’t needed. The concentration of n+ ring is and the numbers of n+ ring and p channel gate are three for the optimal design.n.n.n.n.

• Journal of the Korean Wood Science and Technology
• /
• v.47 no.6
• /
• pp.700-708
• /
• 2019

To verify the possibility of using resistograph to estimate the age of big old living trees, we selected three Zelkova serrata and seven Pinus densiflora in Goesan. The mean diameters at breast height of Z. serrata and P. densiflora were 102 (92-116) cm and 80 (65-110) cm, respectively. The heights measured from the ground using a resistograph ranged at 1.2-4.3 m and 0.6-1.1 m for Z. serrata and P. Densiflora, respectively. The most appropriate needle speed to determine tree-ring boundaries for measuring ring width was 1500 r/min for both tree species. Alternatively, the suitable feed speeds for Z. serrata and P. densiflora were 50 cm/min and 150 cm/min, respectively. From the measured data, the mean numbers of tree rings of Z. serrata and P. densiflora were 57 (43-68) and 104 (93-124), respectively, and the mean tree-ring widths were 4.27 mm (3.18-5.09 mm) and 2.93 mm (2.32-3.34 mm), respectively. A comparison between the time series of tree-ring widths by resistograph and that from the local master chronologies tallied for the heartwood part. Finally, this study showed that resistograph can be used to estimate tree ages when a local master chronology is available.