• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.23-32
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• 2023

Let 𝓢 be a Serre class in the category of modules and 𝖆 an ideal of a commutative Noetherian ring R. We study the containment of Tor modules, Koszul homology and local homology in 𝓢 from below. With these results at our disposal, by specializing the Serre class to be Noetherian or zero, a handful of conclusions on Noetherianness and vanishing of the foregoing homology theories are obtained. We also determine when Tor^R_𝓼+t(R/𝖆, X) ≅ Tor^R_𝓼(R/𝖆, H^𝖆_t(X)).

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.537-544
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• 2003

The non-existence is proved of continuous irreducible representations p : Gal(Q/Q) \longrightarrow GL$_2$(F$_{p}$) with Artin conductor N outside p for a few small values of p and N.N.

• Journal of the Korean Mathematical Society
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• v.38 no.5
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• pp.937-954
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• 2001

This paper is a natural continuation of [2], [3], [4] and [5]. Localization techniques for modular lattices are developed. These techniques are applied to study liftings of linear order types from quotient lattices and to find Г-dense sets in certain lattices without Г-deviation in the sense of [4], where Г is a set of indecomposable linear order types.