• Kyungpook Mathematical Journal
• /
• 제46권4호
• /
• pp.603-613
• /
• 2006

Near-rings considered are right near-rings and R is a near-ring. $J_0^r(R)$, the right Jacobson radical of R of type-0, was introduced and studied by the present authors. In this paper $J_1^r(R)$ and $J_2^r(R)$, the right Jacobson radicals of R of type-1 and type-2 are introduced. It is proved that both $J_1^r$ and $J_2^r$ are radicals for near-rings and $J_0^r(R){\subseteq}J_1^r(R){\subseteq}J_2^r(R)$. Unlike the left Jacobson radical classes, the right Jacobson radical class of type-2 contains $M_0(G)$ for many of the finite groups G. Depending on the structure of G, $M_0(G)$ belongs to different right Jacobson radical classes of near-rings. Also unlike left Jacobson-type radicals, the constant part of R is contained in every right 1-modular (2-modular) right ideal of R. For any family of near-rings $R_i$, $i{\in}I$, $J_{\nu}^r({\oplus}_{i{\in}I}R_i)={\oplus}_{i{\in}I}J_{\nu}^r(R_i)$, ${\nu}{\in}\{1,2\}$. Moreover, under certain conditions, for an invariant subnear-ring S of a d.g. near-ring R it is shown that $J_2^r(S)=S{\cap}J_2^r(R)$.

• 대한수학회보
• /
• 제43권3호
• /
• pp.619-626
• /
• 2006

Let m be any positive integer, R be a ring with identity, $M_m(R)$ be the matrix ring of all m by m matrices eve. R and $G_m(R)$ be the multiplicative group of all n by n nonsingular matrices in $M_m(R)$. In this pape., the following are investigated: (1) for any pairwise coprime ideals ${I_1,\;I_2,\;...,\;I_n}$ in a ring R, $M_m(R/(I_1{\cap}I_2{\cap}...{\cap}I_n))$ is isomorphic to $M_m(R/I_1){\times}M_m(R/I_2){\times}...{\times}M_m(R/I_n);$ and $G_m(R/I_1){\cap}I_2{\cap}...{\cap}I_n))$ is isomorphic to $G_m(R/I_1){\times}G_m(R/I_2){\times}...{\times}G_m(R/I_n);$ (2) In particular, if R is a finite ring with identity, then the order of $G_m(R)$ can be computed.

• 대한수학회보
• /
• 제20권1호
• /
• pp.45-49
• /
• 1983

If R is ring and M is a right (or left) R-module, then M is called a faithful R-module if, for some a in R, x.a=0 for all x.mem.M then a=0. In [4], R.E. Johnson defines that M is a prime module if every non-zero submodule of M is faithful. Let us define that M is of prime type provided that M is faithful if and only if every non-zero submodule is faithful. We call a right (left) ideal I of R is of prime type if R/I is of prime type as a R-module. This is equivalent to the condition that if xRy.subeq.I then either x.mem.I ro y.mem.I (see [5:3:1]). It is easy to see that in case R is a commutative ring then a right or left ideal of a prime type is just a prime ideal. We have defined in [5], that a chain of right ideals of prime type in a ring R is a finite strictly increasing sequence I$_{0}$.contnd.I$_{1}$.contnd....contnd.I$_{n}$; the length of the chain is n. By the right dimension of a ring R, which is denoted by dim, R, we mean the supremum of the length of all chains of right ideals of prime type in R. It is an integer .geq.0 or .inf.. The left dimension of R, which is denoted by dim$_{l}$ R is similarly defined. It was shown in [5], that dim$_{r}$R=0 if and only if dim$_{l}$ R=0 if and only if R modulo the prime radical is a strongly regular ring. By "a strongly regular ring", we mean that for every a in R there is x in R such that axa=a=a$^{2}$x. It was also shown that R is a simple ring if and only if every right ideal is of prime type if and only if every left ideal is of prime type. In case, R is a (right or left) primitive ring then dim$_{r}$R=n if and only if dim$_{l}$ R=n if and only if R.iden.D$_{n+1}$ , n+1 by n+1 matrix ring on a division ring D. in this paper, we establish the following results: (1) If R is prime ring and dim$_{r}$R=n then either R is a righe Ore domain such that every non-zero right ideal of a prime type contains a non-zero minimal prime ideal or the classical ring of ritght quotients is isomorphic to m*m matrix ring over a division ring where m.leq.n+1. (b) If R is prime ring and dim$_{r}$R=n then dim$_{l}$ R=n if dim$_{l}$ R=n if dim$_{l}$ R<.inf. (c) Let R be a principal right and left ideal domain. If dim$_{r}$R=1 then R is an unique factorization domain.TEX>R=1 then R is an unique factorization domain.

• Bulletin of the Korean Chemical Society
• /
• 제11권1호
• /
• pp.31-33
• /
• 1990

We synthesized the novel complexes of (1,1-dimethyl-3,4-diphenyl-1-silacyclopenta-2,4-di ene-2,5-yldibenzene)bis(tricarbonylchromium) and tricarbonyl (R,R'-3,4,5-triphenyl-1-silacyclopenta-2,4-diene-2 -ylbenzene)chromium(R,R' = Me, R = Me/R' = Cl, R = Ph/R' = Cl) from the reaction of the corresponding R,R'-2,3,4,5-Tetraphenyl-1-silacyclopenta-2,4-dien e (abr. R,R'-TPSCp) with chromiumhexacarbonyl. These results reveal that chromium prefer to coordinate to the phenyl substituents of 1-silacyclospentadiene rather than the butadiene moiety of the ring.

• 대한수학회논문집
• /
• 제9권2호
• /
• pp.279-284
• /
• 1994

Let R = ($r_1$, $r_2$, …, $r_{m}$) and S = ($s_1$, $s_2$, …, $s_{n}$ ) be positive integral vectors satisfying $r_1$＋ $r_2$＋…＋ $r_{m}$ = $s_1$＋ $s_2$＋ㆍㆍㆍ＋ $s_{n}$ , and let U(R, S) denote the class of all m $\times$ n matrices A = [$_a{ij}$ ] where $a_{ij}$ = 0 or 1 such that (equation omitted) = $r_{i}$ , (equation omitted) = $s_{j}$ , i = 1, ㆍㆍㆍ, m, j = 1, ㆍㆍㆍ, n.(omitted)

• 한국환경과학회지
• /
• 제9권3호
• /
• pp.223-228
• /
• 2000

충남 서천군 춘장대에서 채취한 갯벌을 통수칼럼에 넣고 오염물질 정화능력을 평가 해 보았다. 각 칼럼에 사용된 시료수는 하수를 G2여과지(6$\mu\textrm{m}$)로 여과한 여액(R1), 생하수를 GF/C여과지(12$\mu\textrm{m}$)로 여과 후 하수중의 미생물에 의한 영향을 제거하기 위하여 고압멸균기(autoclaver)로 12$0^{\circ}C$에서 15분간 멸균한 하수(R2), 여과ㆍ멸균된 하수를 membrane filter로 여과한 해수와 1:1 (하수:해수)로 혼합한 시료수(R3) 그리고 R3에서 사용된 하수와 해수를 이용해 그 비를 1:2로 혼합한 시료수(R4)를 이용하였다. 4종류로 조제된 시험수를 이용한 통수실험 결과를 요약하면 다음과 같다. 통수실험에 의해 제거된 COD 양은 시료수에 하수의 함유량이 증가할수록 증가하였다. 암모니아질소의 경우 각 칼럼에서 580분 실험한 후 총 누적 제거양은 R1 90.1mg, R2 81.0mg, R3 27.6mg, R4 4.1mg이었다. R1과 R2에서 총 누적 제거 양이 해수가 1:1로 함유된 R3보다는 약 3배 높았고, 생하수와 해수가 1:2로 함유된 R4보다는 약 20배 높아 시료수에 하수의 함량이 높을수록 COD와 마찬가지로 암모니아질소가 잘 제거되는 것으로 판단되었다. 총인의 경우 각 칼럼에서 580분 실험한 후 제거된 총 누적 양은 R1 3.4mg, R2 4.2mg, R3 5.6mg, R4 2.0mg이었다. 평균 유입수 농도와 평균 유출수 농도로 구한 Pb의 평균 제거율은 R3와 R4에서 94.6%와 94.9%로 R1과 R2에서의 65.5%와 77.0%보다 약간 높았고, Cd의 평균 제거율도 R3와 R4에서 93.1%와 88.5%로 R1과 R2에서의 61.2%와 82.7%보다 약간 높았다. 이상과 같이 칼럼실험에서 중금속은 해수가 첨가된 시료에서 제거율이 높았다. 하지만 초기 20분간 흡착된 중금속의 양은 580분 동안 흡착된 총 양의 3~4%로 유사한 값을 나타내었다.

• 동의생리병리학회지
• /
• 제19권5호
• /
• pp.1146-1153
• /
• 2005

This study was investigated so that reliability of disease mechanism diagnosis would be examined, the estimation about disease mechanism item of Questionnaires and the relations of disease mechanism would be inquired about 'health diagnosis program' Questionnaires which were used for the object diagnosis of Oriental medicine in the department of Oriental OB&GY, Oriental Medical hospital of Dong-Eui University. We analyzed the results of Questionnaires for 3354 outpatients who had OB & GY disease in the Oriental Medical hospital of Dong-Eui University from April 2000 to March 2004. The diagnosis Questionnaires(after DSOM (r) S.1.1) was the figures 188, the health diagnosis Questionnaires (after DSOM (r) S.1.1) was the figures 137. phiegm deficiency of qi was used in DSOM (r) R.1.1 as it is. The reliability of DSOM (r) S.1.1 was usually higher than DSOM (r) R.1.1 in deficiency of qi blood stasis insufficiency of Yang heat syndrom damp, 5 case disease mechanism. The reliability of DSOM (r) S.1.1 was usually lower than DSOM (r) R.1.1 in blood deficiency stagnation of qi coldness damp dryness liver heart spleen kidney, 8 case disease mechanism. but the great difference wasn't seen, therefore both DSOM (r) S.1.1 and DSOM (r) R.1.1 had similar result. A meeting point both DSOM (r) S.1.1 and DSOM (r) R.1.1 was above 90% in liver spleen blood stasis blood deficiency, 4 case disease mechanism with the exception of phlegm deficiency of Yim nothing of fluctuations of question. A meeting point of coldness that was 82.47% was lowest, A meeting point of the rest disease mechanism was above 85%. The effect that contributed in producing disease mechanism result and in which pure question was over relevance calculation 0.9, insufficiency of Yang damp phlegm that contributed in producing disease mechanism result was lower comparatively in DSOM (r) R.1.1. But the effect that contributed in producing disease mechanism result and in which pure question was over relevance calculation 0.9 except spleen kidney phlegm in DSOM (r) S.1.1

• 미생물학회지
• /
• 제3권1호
• /
• pp.24-26
• /
• 1965

In July, 1963, a virulent outbreak of late blight in the potato field of Daekwanlyung area was studied and it was known as epidemics. Two stocks are $T_1$ and $T_1$ of Phytophthora infestans (Mont.) De Bary which isolated from Irish Cobbler were inoculated at field and green house respectively by cutted leaves method. Two strains have been distinguished in reactions to leaves: $T_1$: Irish Cobbler (r), Morin No. 1 (r) have shown infectivity of disease and Kennebec ($R_1$), 1512-C(16) ($R_2$), Pentland Ace ($R_3$) and Hokkai No. 17 ($R_4$) have not shown infectivity of disease; $T_1$: Irish Cobbler (r), Norin No. I (r) and Kennebec ($R_1$) have shown infectivity of disease and 1512-C (16) ($R_2$), Pentland Ace ($R_3$) and Hokkai No. 17($R_4$) have not shown infectivity of disease. Both are the first record of race O and race 1 of Phytophthora infestans (Mont.) De Bary in Korea.

• 대한수학회보
• /
• 제58권6호
• /
• pp.1341-1354
• /
• 2021

Let r ≥ 2, and let k_i ≥ 2 for 1 ≤ i ≤ r. Mixed van der Waerden's theorem states that there exists a least positive integer w = w(k₁, k₂, k₃, …, k_r; r) such that for any n ≥ w, every r-colouring of [1, n] admits a k_i-term arithmetic progression with colour i for some i ∈ [1, r]. For k ≥ 3 and r ≥ 2, the mixed van der Waerden number w(k, 2, 2, …, 2; r) is denoted by w₂(k; r). B. Landman and A. Robertson [9] showed that for k < r < $\frac{3}{2}$(k - 1) and r ≥ 2k + 2, the inequality w₂(k; r) ≤ r(k - 1) holds. In this note, we establish some results on w₂(k; r) for 2 ≤ r ≤ k.

• Journal of applied mathematics & informatics
• /
• 제5권3호
• /
• pp.819-826
• /
• 1998

The purpose of this paper is to prove the following results; (1) Let R be a prime ring of char $(R)\neq 2$ and I a nonzero left ideal of R. The existence of a nonzero symmetric bi-derivation D : $R\timesR\;\longrightarrow\;$ such that d is sew-commuting on I where d is the trace of D forces R to be commutative (2) Let m and n be integers with $m\;\neq\;0.\;or\;n\neq\;0$. Let R be a noncommutative prime ring of char$ (R))\neq \; 2-1\; p_1 \;n_1$ where p is a prime number which is a divisor of m, and I a nonzero two-sided ideal of R. Let $D_1$ ; $R\;\times\;R\;\longrightarrow\;and\;$ $D_2\;:\;R\;\times\;R\;longrightarrow\;R$ be symmetric bi-derivations. Suppose further that there exists a symmetric bi-additive mapping B ; $R\;\times\;R\;\longrightarrow\;and\;$ such that $md_1(\chi)\chi ＋ n\chi d_2(\chi)=f(\chi$) holds for all $\chi$$\in$I, where $d_1 \;and\; d_2$ are the traces of $D_1 \;and\; D_2$ respectively and f is the trace of B. Then we have $D_1=0 \;and\; D_2=0$.