• Communications of the Korean Mathematical Society
• /
• v.36 no.2
• /
• pp.229-238
• /
• 2021

Let R be a ring with characteristic different from 2. An additive mapping F : R → R is called a generalized derivation on R if there exists a derivation d : R → R such that F(xy) = F(x)y + xd(y) holds for all x, y ∈ R. In the present paper, we show that if R is a prime ring satisfying certain identities involving a generalized derivation F associated with a derivation d, then R becomes commutative and in some cases d comes out to be zero (i.e., F becomes a left centralizer). We provide some counter examples to justify that the restrictions imposed in the hypotheses of our theorems are not superfluous.

• Journal of applied mathematics & informatics
• /
• v.40 no.5_6
• /
• pp.915-923
• /
• 2022

The purpose of the present paper is to obtain commutativity of prime Γ-near-ring N with generalized derivations F and G with associated derivations d and h respectively satisfying one of the following conditions:(i) G([x, y]α = ±f(y)α(xoy)βγg(y), (ii) F(x)βG(y) = G(y)βF(x), for all x, y ∈ N, β ∈ Γ (iii) F(u)βG(v) = G(v)βF(u), for all u ∈ U, v ∈ V, β ∈ Γ,(iv) if 0 ≠ F(a) ∈ Z(N) for some a ∈ V such that F(x)αG(y) = G(y)αF(x) for all x ∈ V and y ∈ U, α ∈ Γ.

• Kyungpook Mathematical Journal
• /
• v.62 no.3
• /
• pp.595-613
• /
• 2022

Let R be a commutative ring with identity and let I be a proper ideal of R. In this paper, we study the ideal based extended zero-divisor graph 𝚪'_I (R) and prove that 𝚪'_I (R) is connected with diameter at most two and if 𝚪'_I (R) contains a cycle, then girth is at most four girth at most four. Furthermore, we study affinity the connection between the ideal based extended zero-divisor graph 𝚪'_I (R) and the ideal-based zero-divisor graph 𝚪_I (R) associated with the ideal I of R. Among the other things, for a radical ideal of a ring R, we show that the ideal-based extended zero-divisor graph 𝚪'_I (R) is identical to the ideal-based zero-divisor graph 𝚪_I (R) if and only if R has exactly two minimal prime-ideals which contain I.

• Journal of Industrial Technology
• /
• v.36
• /
• pp.65-69
• /
• 2016

Deflection of the vertical is used in geodetic surveying associated with geoid network construction for geoid modeling and ellipsoid decision and obtained by gravity survey, astronomic survey etc. Technique of astronomic survey and gravity survey is very complex and requires a significant amount of time until gathering data. So this study is to determined a various method which evaluates deflection of the vertical and components about deflection of the vertical using GPS results and orthometric height value decided by leveling. Results of components about deflection of the vertical using GPS/leveling is that ${\xi}$ conponent is distributed $-2.11^{{\prime}{\prime}}{\pm}0.62$, ${\eta}$ component is distributed $1.75^{{\prime}{\prime}}{\pm}0.71$. Decision of component about deflection of the vertical using GPS is less complex than existing astronomic survey. Decision of component about deflection of vertical line using GPS is not complicated than astronomic surveying and can determine in a very short time. So it will be important means to determine the exact orthometric height, topographic study and diastrophism if can periodically calculate.

• Journal of Korean Society on Water Environment
• /
• v.25 no.5
• /
• pp.697-703
• /
• 2009

In this study, changes in the composition of dissolved organic carbon (DOC) were investigated using water samples collected at a downstream site of the Namhan River near the Lake Paldang ($N37^{\circ}24^{\prime}05.33^{{\prime}{\prime}}E127^{\circ}32^{\prime}25.01^{{\prime}{\prime}}$) during a heavy rain event from July 23 to July 28, 2008. The DOC concentrations varied from 1.68 to 3.18 mg/L with the maxium value at a peak of the river water level. Each DOC sample was fractionated into three compositions including hydrophilic (Hi), hydrophobic acid (HoA) and hydrophobic neutral (HoN) fractions. The results showed that HoA was most abundant fractions, constituting 47.2~56.5% of DOC. Refractory dissolved organic carbon (R-DOC) contents were also determined by measuring the DOC concentration after 28-day dark incubation of the samples. R-DOC content was in the range from 83 to 99% of DOC and it was significantly correlated with HoA contents (r = 0.91, p<0.005), while it did not exhibit such a good correlation with the fractions of Hi and HoN (p>0.02). Our results suggest that the HoA, which is associated with humic substances, may be a major composition of refractory organic matters in rivers during storm events.

• Korean Journal of Mathematics
• /
• v.30 no.2
• /
• pp.187-198
• /
• 2022

In this paper, we introduce a new concept in number theory called ζ-factors associated with a positive integer n. Applications of ζ-factors are in the arrangement of the defining polynomials in cyclic n-roots algebraic system and are thoroughly investigated. More precisely, ζ-factors arise in the proofs of vanishing theorems in regard to associated prime factors of the system. Exact computations through concrete examples of positive dimensions for n = 16, 18 support the results.

• Journal of the Chungcheong Mathematical Society
• /
• v.9 no.1
• /
• pp.61-68
• /
• 1996

We investigate associated prime ideals of the module of generalized fractions defined by poor essential sequences and extend the McAdam and Ratliff's criterion of locally unmixed rings.

• Honam Mathematical Journal
• /
• v.32 no.4
• /
• pp.675-687
• /
• 2010

In this paper the dual notion of tight closure of ideals relative to modules is introduced and some related results are obtained.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.1
• /
• pp.103-108
• /
• 2000

Using spectral sequences we calculate the highest nonvanishing index of Tor for modules of finite projective dimension. The result is applied to compute the depth of the highest nonvanishing Tor. This is one of the cases when a problem of Auslander is positive.

• Journal of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1167-1182
• /
• 2016

Let M be an R-module, where R is a commutative ring with identity 1 and let G(V,E) be a graph. In this paper, we study the graphs associated with modules over commutative rings. We associate three simple graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ to M called full annihilating, semi-annihilating and star-annihilating graph. When M is finite over R, we investigate metric dimensions in $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$. We show that M over R is finite if and only if the metric dimension of the graph $ann_f({\Gamma}(M_R))$ is finite. We further show that the graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ are empty if and only if M is a prime-multiplication-like R-module. We investigate the case when M is a free R-module, where R is an integral domain and show that the graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ are empty if and only if $$M{\sim_=}R$$. Finally, we characterize all the non-simple weakly virtually divisible modules M for which Ann(M) is a prime ideal and Soc(M) = 0.