• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.913-920
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• 2004

We give a characterization for fundamental groups of graphs of groups amalgamating cyclic edge subgroups to be cyclic subgroup separable if each pair of edge subgroups has a non-trivial intersection. We show that fundamental groups of graphs of abelian groups amalgamating cyclic edge subgroups are cyclic subgroup separable, hence residually finite, if each edge subgroup is isolated in its containing vertex group.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.443-450
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• 2011

In this paper, we construct a Gorenstein Artinian algebra R/J with non-unimodal Hilbert function h = (1, 13, 12, 13, 1) to investigate the algebraic structure of the ideal J in a polynomial ring R. For this purpose, we use a software system Macaulay 2, which is devoted to supporting research in algebraic geometry and commutative algebra.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1189-1201
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• 2011

Let R be a ring and M a right R-module, S = $End_R$(M). The module M is called almost principally small injective (or APS-injective for short) if, for any a ${\in}$ J(R), there exists an S-submodule $X_a$ of M such that $l_Mr_R$(a) = Ma $Ma{\bigoplus}X_a$ as left S-modules. If $R_R$ is a APS-injective module, then we call R a right APS-injective ring. We develop, in this paper, APS-injective rings as a generalization of PS-injective rings and AP-injective rings. Many examples of APS-injective rings are listed. We also extend some results on PS-injective rings and AP-injective rings to APS-injective rings.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.93-104
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• 2024

Let R be a commutative ring with identity. In this paper, we introduce a new class of ideals called the class of strongly quasi J-ideals lying properly between the class of J-ideals and the class of quasi J-ideals. A proper ideal I of R is called a strongly quasi J-ideal if, whenever a, b ∈ R and ab ∈ I, then a² ∈ I or b ∈ Jac(R). Firstly, we investigate some basic properties of strongly quasi J-ideals. Hence, we give the necessary and sufficient conditions for a ring R to contain a strongly quasi J-ideals. Many other results are given to disclose the relations between this new concept and others that already exist. Namely, the primary ideals, the prime ideals and the maximal ideals. Finally, we give an idea about some strongly quasi J-ideals of the quotient rings, the localization of rings, the polynomial rings and the trivial rings extensions.

• Journal of Communications and Networks
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• v.7 no.4
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• pp.509-524
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• 2005

Due to the strict requirements of emerging applications, per-flow admission control is gaining increasing importance. One way to implement per-flow admission control is using an on­path resource reservation protocol, where the admission decision is made hop-by-hop after a new flow request arrives at the network boundary. The next-steps in signaling (NSIS) working group of the Internet engineering task force (IETF) is standardising such an on-path signaling protocol. One of the reservation methods considered by NSIS is reduced-state mode, which, suiting the differentiated service (DiffServ) concept, only allows per-class states in interior nodes of a domain. Although there are clear benefits of not dealing with per-flow states in interior nodes-like scalability and low complexity-, without per-flow states the handling of re-routed flows, e.g., after a failure, is a demanding and highly non-trivial task. To be applied in carrier-grade networks, the protocol needs to be resilient in this situation. In this article, we will explain the consequences of a route failover to resource reservation protocols: Severe congestion and incorrect admission decisions due to outdated reservation states. We will set requirements that handling solutions need to fulfill, and we propose extensions to reduced-state protocols accordingly. We show with a set of simulated scenarios that with the given solutions reduced-state protocols can handle re-routed flows practically as fast and robust as stateful protocols.