• Journal of Ocean Engineering and Technology
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• v.24 no.2
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• pp.47-52
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• 2010

The proper surface pressure on the pistons rings in the diesel engine of a ship is very important, because the pressure controls the oil that is needed to maintain friction at acceptable levels between the pistons and the cylinders. In this paper, basic and theoretical concepts to compute the ring pressure were formulated and applied to obtain the proper surface pressures on selected sample piston rings. During the calculation of the pressure on the piston rings, the computation of the accurate free shape of the piston ring was required. Earlier, Arnold and Prescott introduced theories to compute the free shapes of piston rings, and their approach used rectangular and polar coordinates. In this paper, the free shapes of piston rings using two different theories were computed and compared. The results were quite close, representing the free shape of the piston ring. Ring pressure was computed using the Arnold's free shape that was obtained. A simple GUI was made to compute the surface pressure on the piston rings.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.457-470
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• 2005

Yu showed that every right (left) primitive factor ring of weakly right (left) duo rings is a division ring. It is not difficult to show that each weakly right (left) duo ring is abelian and has the classical right (left) quotient ring. In this note we first provide a left duo ring (but not weakly right duo) in spite of it being left Noetherian and local. Thus we observe conditions under which weakly one-sided duo rings may be two-sided. We prove that a weakly one-sided duo ring R is weakly duo under each of the following conditions: (1) R is semilocal with nil Jacobson radical; (2) R is locally finite. Based on the preceding case (1) we study a kind of composition length of a right or left Artinian weakly duo ring R, obtaining that i(R) is finite and $\alpha^{i(R)}R\;=\;R\alpha^{i(R)\;=\;R\alpha^{i(R)}R\;for\;all\;\alpha\;{\in}\;R$, where i(R) is the index (of nilpotency) of R. Note that one-sided Artinian rings and locally finite rings are strongly $\pi-regular$. Thus we also observe connections between strongly $\pi-regular$ weakly right duo rings and related rings, constructing available examples.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.407-464
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• 2023

Let R be a commutative ring with identity. The structure theorem says that R is a PIR (resp., UFR, general ZPI-ring, π-ring) if and only if R is a finite direct product of PIDs (resp., UFDs, Dedekind domains, π-domains) and special primary rings. All of these four types of integral domains are Krull domains, so motivated by the structure theorem, we study the prime factorization of ideals in a ring that is a finite direct product of Krull domains and special primary rings. Such a ring will be called a general Krull ring. It is known that Krull domains can be characterized by the star operations v or t as follows: An integral domain R is a Krull domain if and only if every nonzero proper principal ideal of R can be written as a finite v- or t-product of prime ideals. However, this is not true for general Krull rings. In this paper, we introduce a new star operation u on R, so that R is a general Krull ring if and only if every proper principal ideal of R can be written as a finite u-product of prime ideals. We also study several ring-theoretic properties of general Krull rings including Kaplansky-type theorem, Mori-Nagata theorem, Nagata rings, and Noetherian property.

• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.587-592
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• 2003

A near-ring N is called strongly reduced if, for $a{\in}N$, $a^2{\in}N_c$ implies $a{\in}N_c$, where $N_c$ denotes the constant part of N. We investigate some properties of strongly reduced near-rings and apply those to the study of left strongly regular near-rings. Finally we classify all reduced, and strongly reduced near-rings of order ${\leq}7$.

• East Asian mathematical journal
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• v.34 no.1
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• pp.39-46
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• 2018

In this article we consider rings whose Jacobson radical contains all the nilpotent elements, and call such a ring an NJ-ring. The class of NJ-rings contains NI-rings and one-sided quasi-duo rings. We also prove that the Koethe conjecture holds if and only if the polynomial ring R[x] is NJ for every NI-ring R.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.57-64
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• 2020

Let R ⊆ T be an ascending chain of commutative rings with identity and H(R, T) (resp., h(R, T)) the composite Hurwitz series ring (resp., composite Hurwitz polynomial ring). In this article, we give some conditions for the rings H(R, T) and h(R, T) to be PS-rings.

• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.303-310
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• 2006

M. $Bre\v{s}ar$ and J. Vukman obtained some results concerning orthogonal derivations in semiprime rings which are related to the result that is well-known to a theorem of Posner for the product of two derivations in prime rings. In this paper, we present orthogonal generalized derivations in semiprime near-rings.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.151-156
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• 2007

A connection between weak ${\pi}-regularity$ and the condition every prime ideal is maximal will be investigated. We prove that a certain 2-primal ring R is weakly ${\pi}-regular$ if and only if every prime ideal is maximal. This result extends several known results nontrivially. Moreover a characterization of minimal prime ideals is also considered.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1251-1258
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• 2020

This paper establishes a formula changing the ring from a Noetherian local ring A of dimension d > 0 containing the residue field k to the polynomial ring in d variables k[X₁, X₂, …, X_d] for mixed multiplicities. And as consequences, we get a formula for the multiplicity of Rees rings and formulas for mixed multiplicities and the multiplicity of Rees rings of quotient rings of A by highest dimensional associated prime ideals of A.

• Journal for History of Mathematics
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• v.19 no.3
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• pp.85-94
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• 2006

We review Galois rings and permutation polynomials over Galois rings with emphasis on cryptological properties of Dickson polynomials and conclude that it is not plausible to obtain the Dickson scheme which has a Galois ring as a plaintext space.