• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.59-66
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• 2008

Keskin and Harmanci defined the family B(M,X) = ${A{\leq}M|{\exists}Y{\leq}X,{\exists}f{\in}Hom_R(M,X/Y),\;Ker\;f/A{\ll}M/A}$. And Orhan and Keskin generalized projective modules via the class B(M, X). In this note we introduce X-local summands and X-hollow modules via the class B(M, X). Let R be a right perfect ring and let M be an X-lifting module. We prove that if every co-closed submodule of any projective module P contains Rad(P), then M has an indecomposable decomposition. This result is a generalization of Kuratomi and Chang's result [9, Theorem 3.4]. Let X be an R-module. We also prove that for an X-hollow module H such that every non-zero direct summand K of H with $K{\in}B$(H, X), if $H{\oplus}H$ has the internal exchange property, then H has a local endomorphism ring.

• The KIPS Transactions:PartC
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• v.11C no.4
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• pp.497-508
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• 2004

The existing wireless LAN standard IEEE802.11b has many vulnerabilities from security point of view. The authentication mechanisms in IEEE802.11b have many vulnerabilities. As a result to complement the weak of IEEE802.11b authentication, the IEEE802.1x had been developed in the sense of providing strong user authentication with appropriate mechanism. But this mechanism does not perform AP authentication and there are also some weak points. And in confidentiality and message Integrity case, WEP is weak from key stream reuse attack, IV reuse attack and so on. For that reason, in this paper we propose secure wireless LAN system. Our system provides strong user authentication, confidentiality, and message integrity based on existing IEEE802.1x framework and TLS.