• 대한수학회보
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• 제58권3호
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• pp.689-698
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• 2021

In this paper, we show some results on the artinianness of local cohomology modules with respect to a system of ideals. If M is a 𝚽-minimax ZD-module, then H^{dim M}_𝚽(M)/𝖆H^{dim M}_𝚽(M) is artinian for all 𝖆 ∈ 𝚽. Moreover, if M is a 𝚽-minimax ZD-module, t is a non-negative integer and Hⁱ_𝚽(M) is minimax for all i > t, then Hⁱ_𝚽(M) is artinian for all i > t.

• 대한수학회보
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• 제51권6호
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• pp.1851-1861
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• 2014

We introduce the concept of w-zero-divisor (w-ZD) rings and study its related rings. In particular it is shown that an integral domain R is an SM domain if and only if R is a w-locally Noetherian w-ZD ring and that a commutative ring R is w-Noetherian if and only if the polynomial ring in one indeterminate R[X] is a w-ZD ring. Finally we characterize universally zero divisor rings in terms of w-ZD modules.