• Communications of the Korean Mathematical Society
• /
• v.30 no.4
• /
• pp.363-377
• /
• 2015

Let R be a ring, (S,${\leq}$) a strictly ordered monoid and ${\omega}$ : S ${\rightarrow}$ End(R) a monoid homomorphism. The skew generalized power series ring R[[S,${\omega}$]] is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings, and Mal'cev-Neumann Laurent series rings. In this paper, we investigate the interplay between the ring-theoretical properties of R[[S,${\omega}$]] and the graph-theoretical properties of its zero-divisor graph ${\Gamma}$(R[[S,${\omega}$]]). Furthermore, we examine the preservation of diameter and girth of the zero-divisor graph under extension to skew generalized power series rings.

• Korean Journal of Mathematics
• /
• v.17 no.2
• /
• pp.189-196
• /
• 2009

Let D be an integral domain, and let U be a group of units of D. Let $D^*=D-\{0\}$ and ${\Gamma}=D^*/U$ be the commutative cancellative semigroup under aU+bU=abU. We prove that $Cl(D)=Cl({\Gamma})$ and that D is a PvMD (resp., GCD-domain, Mori domain, Krull domain, factorial domain) if and only if ${\Gamma}$ is a PvMS(resp., GCD-semigroup, Mori semigroup, Krull semigroup, factorial semigroup). Let U=U(D) be the group of units of D. We also show that if D is integrally closed, then $D[{\Gamma}]$, the semigroup ring of ${\Gamma}$ over D, is an integrally closed domain with $Cl(D[{\Gamma}])=Cl(D){\oplus}Cl(D)$; hence D is a PvMD (resp., GCD-domain, Krull domain, factorial domain) if and only if $D[{\Gamma}]$ is.

• Nuclear Engineering and Technology
• /
• v.31 no.4
• /
• pp.423-431
• /
• 1999

A radiotracer technique has been developed to monitor the rotational movement of two piston rings in one cylinder during engine operation. The rings were labeled with two different kinds of radioisotopes, i.e. $^{60}$ Co and $^{192}$ Ir, for identification of the top ring from the second ring. The radiotracers were implanted in a small hole bored on the inner side of each piston ring. The rings were installed in a single cylinder hydrogen engine and three Nal scintillation detectors were mounted around the engine block to measure the gamma radiation. The angle of ring-gap orientation was determined from the radiation counts measured with the three detectors during engine operation. Two windows (upper window for $^{60}$ Co and lower window for $^{192}$ Ir) were set on each ratemeter to count radiation from the two isotopes separately. Procedure to convert the radiation counts to the position of the ring gap was established. With the software programmed with MS-Visualbasic, radiation counts were compared with the reference responses that were measured at angular intervals of 10$^{\circ}$for each piston ring in advance of the experiment. The result was used for the evaluation of the relationship between the orientation of ring-gaps and oil consumption. It was found that an increase in the oil consumption rate of a specific operation condition was closely related to the relative phase angle of the two piston rings.

• YAKHAK HOEJI
• /
• v.39 no.2
• /
• pp.175-184
• /
• 1995

The interaction of omeprazole(OMP) with $\gamma$-cyclodextrin($\gamma$-CyD) was investigated by solubility study and the complexation was confirmed by means of UV/VIS spectrophotometer, circular dichroism, differential scanning calorimeter, and $^{1}$H nuclear magnetic resonance spectra. The stability, dissolution rate, and partition coefficient of the complex were measured. The results present that the benzimidazole moiety and a part of pyridine ring containing sulfur atom of OMP might be included into the cavity of $\gamma$-CyD and the formation type of inclusion complex appeared to be B$_{s}$. The stoichiometric ratio of OMP to $\gamma$-CyD in the complex was found to be 1:1 and the stability constant of the complex found to be 97.1 M$^{-1}$. And the dissolution rate of OMP was markedly increased by inclusion complex formation with $\gamma$-CyD, and so it was above 90% in 5 min. from solid complex. Oil to water partition coefficient of OMP-$\gamma$-CyD complex was 60, which is significantly higher than that of OMP itself, 36.4. The degradation rate constant of OMP were greater than OMP-$\gamma$-CyD complex in aqueous solutions of various pHs, and the half lives of OMP and OMP-$\gamma$-CyD at pH 9 were 279.2 and 509.9 days, respectively, showing that the complex was more stable than OMP, therefore it was thought that OMP was stabilized by inclusion formation with $\gamma$-CyD.

• Journal of the Korean Mathematical Society
• /
• v.52 no.2
• /
• pp.417-429
• /
• 2015

Let R be a commutative ring with unity. The annihilator ideal graph of R, denoted by ${\Gamma}_{Ann}(R)$, is a graph whose vertices are all non-trivial ideals of R and two distinct vertices I and J are adjacent if and only if $I{\cap}Ann(J){\neq}\{0\}$ or $J{\cap}Ann(I){\neq}\{0\}$. In this paper, we study some connections between the graph-theoretic properties of this graph and some algebraic properties of rings. We characterize all rings whose annihilator ideal graphs are totally disconnected. Also, we study diameter, girth, clique number and chromatic number of this graph. Moreover, we study some relations between annihilator ideal graph and zero-divisor graph associated with R. Among other results, it is proved that for a Noetherian ring R if ${\Gamma}_{Ann}(R)$ is triangle free, then R is Gorenstein.

• Korean Journal of Mathematics
• /
• v.22 no.1
• /
• pp.181-206
• /
• 2014

Let $R={\bigoplus}_{\alpha{\in}\Gamma}R_{\alpha}$ be a graded integral domain graded by an arbitrary grading torsionless monoid ${\Gamma}$, and ⋆ be a semistar operation on R. In this paper we define and study the graded integral domain analogue of ⋆-Nagata and Kronecker function rings of R with respect to ⋆. We say that R is a graded Pr$\ddot{u}$fer ⋆-multiplication domain if each nonzero finitely generated homogeneous ideal of R is ⋆$_f$-invertible. Using ⋆-Nagata and Kronecker function rings, we give several different equivalent conditions for R to be a graded Pr$\ddot{u}$fer ⋆-multiplication domain. In particular we give new characterizations for a graded integral domain, to be a $P{\upsilon}MD$.

• Korean Journal of Mathematics
• /
• v.19 no.3
• /
• pp.255-261
• /
• 2011

Let D be an integral domain, S be a torsion-free grading monoid such that the quotient group of S is of type (0, 0, 0, ${\ldots}$), and D[S] be the semigroup ring of S over D. We show that D[S] is an H-domain if and only if D is an H-domain and each maximal t-ideal of S is a $v$-ideal. We also show that if $\mathbb{R}$ is the eld of real numbers and if ${\Gamma}$ is the additive group of rational numbers, then $\mathbb{R}[{\Gamma}]$ is not an H-domain.

• 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.

• Journal of applied mathematics & informatics
• /
• v.40 no.3_4
• /
• pp.729-740
• /
• 2022

Let ℤ be the ring of integers and let ℤ_n be the ring of integers modulo n. Let ℤ(+)ℤ_n be the idealization of ℤ_n in ℤ and let (ℤ(+)ℤ_n)[X]] be either (ℤ(+)ℤ_n)[X] or (ℤ(+)ℤ_n)[[X]]. In this article, we study the zero-divisor graphs of ℤ(+)ℤ_n and (ℤ(+)ℤ_n)[X]]. More precisely, we completely characterize the diameter and the girth of the zero-divisor graphs of ℤ(+)ℤ_n and (ℤ(+)ℤ_n)[X]]. We also calculate the chromatic number of the zero-divisor graphs of ℤ(+)ℤ_n and (ℤ(+)ℤ_n)[X]].

• Archives of Pharmacal Research
• /
• v.12 no.1
• /
• pp.17-21
• /
• 1989

We have reported earlier on the reactivity of 7-dithiocarboxy-3-phenyl-5,6-dihydro imidazo[2,1-b]thiazolium-betaine with several para-substituted phenacyl bromides. In this work reactions of 7-dithiocarboxy-3-phenyl(or methyl)-5,6-dihydro imidazo[2,1-b]thiazolium-betaine with a series of aliphatic alkylating agents of ${\alpha}$ -halo ketone,${\gamma}$-halo koto ester and ${\alpha}$ -halo ester were examined for the similar purpose. In case of ${\alpha}$-halo ketone or ${\gamma}$-halo koto ester such as ${\alpha}$ -chloro acetone or ethyl 4-chloro acetoacetate new biheterocyclic compound was obtained via ring transformation reaction. However, reaction of the betaine with methyl(or ethyl) bromoacetate used as a ${\alpha}$-halo ester, gave, in-stead, S-alkylated quarternary ammonium salt.