• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.11-19
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• 2023

Let 𝓗₀ be the set of rings R such that Nil(R) = Z(R) is a divided prime ideal of R. The concept of maximal non φ-chained subrings is a generalization of maximal non valuation subrings from domains to rings in 𝓗₀. This generalization was introduced in [20] where the authors proved that if R ∈ 𝓗₀ is an integrally closed ring with finite Krull dimension, then R is a maximal non φ-chained subring of T(R) if and only if R is not local and |[R, T(R)]| = dim(R) + 3. This motivates us to investigate the other natural numbers n for which R is a maximal non φ-chained subring of some overring S. The existence of such an overring S of R is shown for 3 ≤ n ≤ 6, and no such overring exists for n = 7.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.935-946
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• 2015

The purpose of this paper is to introduce a new class of rings that is closely related to the classes of pseudo valuation rings (PVRs) and pseudo-almost valuation domains (PAVDs). A commutative ring R is said to be ${\phi}$-ring if its nilradical Nil(R) is both prime and comparable with each principal ideal. The name is derived from the natural map ${\phi}$ from the total quotient ring T(R) to R localized at Nil(R). A prime ideal P of a ${\phi}$-ring R is said to be a ${\phi}$-pseudo-strongly prime ideal if, whenever $x,y{\in}R_{Nil(R)}$ and $(xy){\phi}(P){\subseteq}{\phi}(P)$, then there exists an integer $m{\geqslant}1$ such that either $x^m{\in}{\phi}(R)$ or $y^m{\phi}(P){\subseteq}{\phi}(P)$. If each prime ideal of R is a ${\phi}$-pseudo strongly prime ideal, then we say that R is a ${\phi}$-pseudo-almost valuation ring (${\phi}$-PAVR). Among the properties of ${\phi}$-PAVRs, we show that a quasilocal ${\phi}$-ring R with regular maximal ideal M is a ${\phi}$-PAVR if and only if V = (M : M) is a ${\phi}$-almost chained ring with maximal ideal $\sqrt{MV}$. We also investigate the overrings of a ${\phi}$-PAVR.

• The Transactions of the Korea Information Processing Society
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• v.2 no.6
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• pp.879-890
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• 1995

This paper proposes the shuttle protocol that can gather management information from managed systems in an efficient way. In this paper, we implement the protocol and evaluate the performance by simulation. The major feature of the shuttle protocol is a chained logical connection through managed systems, and management informations to be collected are circulated among specified managed systems in circular order on a logical ring connection. The data generated by an managed system are relayed to a neighbor managed system and the system sends its data which has additional management information to received data. Finally, a manager stationman get all of data generated by every managed system. we will show the analysis of management traffic patterns using conventional polling schemes and the shuttle protocol implementation viable to TCP/IP network and improving existing polling mechansims. Additionally, it is performed to evaluate the packet processing time and its distribution of a manager system and a gateway, and the queue length of packet and bit length of gateway against conventional polling schemes by simulation using OPNRT, a simulation-dedicated package.