• Journal of the Korean Mathematical Society
• /
• v.52 no.4
• /
• pp.839-851
• /
• 2015

A *-ring R is called (strongly) *-clean if every element of R is the sum of a projection and a unit (which commute with each other). In this note, some properties of *-clean rings are considered. In particular, a new class of *-clean rings which called strongly ${\pi}$-*-regular are introduced. It is shown that R is strongly ${\pi}$-*-regular if and only if R is ${\pi}$-regular and every idempotent of R is a projection if and only if R/J(R) is strongly regular with J(R) nil, and every idempotent of R/J(R) is lifted to a central projection of R. In addition, the stable range conditions of *-clean rings are discussed, and equivalent conditions among *-rings related to *-cleanness are obtained.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.4
• /
• pp.945-956
• /
• 2020

We introduce the concept of S-exchange rings to unify various subclass of exchange rings, where S is a subset of the ring. Many properties on S-exchange rings are obtained. For instance, we show that a ring R is clean if and only if R is left U(R)-exchange, a ring R is nil clean if and only if R is left (N(R) - 1)-exchange, and that a ring R is J-clean if and only if R is left (J(R) - 1)-exchange. As a conclusion, we obtain a sufficient condition such that clean (nil clean property, respectively) can pass to corners and reprove that J-clean passes to corners by a different way.

• Journal of the Korean Mathematical Society
• /
• v.57 no.1
• /
• pp.113-129
• /
• 2020

In this paper, we study the Poisson cohomology ring of the tensor product of Poisson algebras. Explicitly, it is proved that the Poisson cohomology ring of tensor product of two Poisson algebras is isomorphic to the tensor product of the respective Poisson cohomology ring of these two Poisson algebras as Gerstenhaber algebras.

• Journal of Integrative Natural Science
• /
• v.7 no.4
• /
• pp.278-282
• /
• 2014

We define a numerical invariant $row^*_j(A)$ over Cohen-Macaulay local ring A, which is related to the presenting matrices of the j-th syzygy module (with or without free summands). We show that $row_d(A)$=$row_{CM}(A)$ and $row^*_d(A)$=$row^*_{CM}(A)$ for a Cohen-Macaulay local ring A of dimension d.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.4
• /
• pp.599-608
• /
• 2004

Let R be an associative ring with identity and J(R) be the Jacobson radical of R. In this paper we investigate the generalization of the Jacobson radical of R, J＊ (R) say. Also we study the rings that J＊(R) = J(R).

• Transactions of Materials Processing
• /
• v.19 no.8
• /
• pp.494-501
• /
• 2010

The main objective of this study is to examine the sensitivity of calibration curves of FEA of ring compression test to frictional shear factor. Ring compression test has been investigated by measuring dimensional changes at different positions of ring specimen and they include the changes in internal diameter at the middle and top section of the specimen, outer diameter at the middle and top section, surface expansion at the top surface, respectively. Initial ring geometries employed in analysis maintain a fixed ratio of 6 : 3 : 2, i.e. outer diameter : inner diameter : thickness of the ring specimen, which is generally known as 'standard' specimen. A rigid plastic material for different work-hardening characteristics has been modeled for simulations using rigid-plastic finite element code. Analyses have been performed within a definite range of friction as well as over whole range of friction to show different sensitivities to the interfacial friction for different ranges of friction. The results of investigation in this study have been summarized in terms of a dimensionless gradient. It has been known from the results that the dimensional changes at different positions of ring specimen show different linearity and sensitivity to the frictional condition on the contact surface.

• Transactions of Materials Processing
• /
• v.17 no.5
• /
• pp.343-349
• /
• 2008

The wear between piston ring face and cylinder liner is an extremely unpredictable and hard-to-reproduce phenomenon that significantly decreases engine performance. This study will discuss characteristics of wear between hard and soft piston ring coatings with running surface of cylinder liner. Detailed tribological analysis by using Pin-on-Disk(POD) testing machine describes the lubricity mechanism between piston ring coatings and cylinder liner at different temperature with and without oil. The effect of surface roughness of the cylinder liner on the friction coefficient and wear amount of piston ring coatings will also be analyzed. To simulate scuffing mechanism between piston ring and cylinder liner, accelerated lab testing was performed. This study will provide the data from tribological testing of hard and soft piston ring coatings against cylinder liner. Furthermore, the microstructures and morphological features of the surface and the near-surface materials during wear will be investigated. From the scuffing test by using POD testing machine, scuffing mechanisms for the soft and hard coating will be analyzed and experimentally confirmed.

• Transactions of Materials Processing
• /
• v.16 no.3 s.93
• /
• pp.172-177
• /
• 2007

The process design for large-scale ring rolling of Ti-6Al-4V alloy was performed by calculation method, processing map approach and FEM simulation. The ring rolling design includes geometry design and optimization of process variables. The calculation method was used to make geometry design such as initial billet and blank sizes, and final rolled ring shape. A commercial FEM code, SHAPE-RR was used to simulate the effect of process variables in ring rolling on the distribution of the internal state variables such as strain, strain rate and temperature. In order to predict the forming defects during ring rolling and the formation of over-heating above $\beta$-transus temperature due to deformation heating, the process-map approach based on Ziegler's instability criterion was used with FEM simulation. Finally, an optimum process design to obtain sound Ti-6Al-4V rings without forming defects was suggested through combined approach of Ziegler's instability map and FEM simulation results.

• Bulletin of the Korean Chemical Society
• /
• v.19 no.5
• /
• pp.569-575
• /
• 1998

Investigation of the structure of the gangliosides has proven to be very important in the understanding of their biological roles. We have determined the tertiary structure of asialoganglioside GM1 $(GA_1)$ using NMR spectroscopy and distance geometry calculations. All of the structures are very similar except the glycosidic torsion angles in the ring IV and ring III linkages. There are two low-energy structures for GA1, G1 and G2. G1 differs from G2 only in the IV-III glycosidic linkages and the orientation of acetamido group in ring III. There is a stable intramolecular hydrogen bond between the third hydroxyl group in ring I and the ring oxygen atom in ring II. Also, there may be a weak hydrogen bond between the second hydroxyl group in ring IV and the acetamido group in ring III. Small coupling constants of $^3J_{IH3,IOH3}\; and\; ^3J_{IVH2,IVOH2}$ support this result. Overall structural features of $(GA_1)$ are very similar to those of $(GM_1)$. It implicates that specificities of the sugar moieties in GM1 are caused not by their tertiary foldings, but mainly by the electrostatic interactions between the polar sialic acid and its receptors. Since it is evident that $(GA_1)$ is more hydrophobic than $(GA_1)$, a receptor with a hydrophobic binding site can recognize the $(GA_1)$ better than $(GA_1)$. Studies on the conformational properties of $(GA_1)$ may lead to a better understanding of the molecular basis of its functions.

• Journal of the Korean Mathematical Society
• /
• v.60 no.2
• /
• pp.327-339
• /
• 2023

Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. In this article we introduce a new class of ring, called S-multiplication rings which are S-versions of multiplication rings. An R-module M is said to be S-multiplication if for each submodule N of M, sN ⊆ JM ⊆ N for some s ∈ S and ideal J of R (see for instance [4, Definition 1]). An ideal I of R is called S-multiplication if I is an S-multiplication R-module. A commutative ring R is called an S-multiplication ring if each ideal of R is S-multiplication. We characterize some special rings such as multiplication rings, almost multiplication rings, arithmetical ring, and S-P IR. Moreover, we generalize some properties of multiplication rings to S-multiplication rings and we study the transfer of this notion to various context of commutative ring extensions such as trivial ring extensions and amalgamated algebras along an ideal.