• 호남수학학술지
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• 제1권1호
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• pp.61-75
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• 1979

n-차원(次元) $C^{**}$ 다양체(多樣體)에서 얻어진 미분형식(微分形式)과 외미분(外微分)에 의하여 Rhan complex가 얻어지고 이것으로부터 얻어진 Cohomology를 Rham cohomology라 한다. n차원(次元) $C^{**}$ 다양체(多樣體)의 위상적(位相的) 구조(構造)만으로 정의(定義)되여진 Čech cohomology가 있는바 이것은 다양체(多樣體)의 피복(被覆)에 따라 그 cohomology 군(群)이 달라지는 것이 흠이다. 여기서는 Rham cohomology와 단순피복(單純被覆)을 취(取)하였을때의 Čech cohomology가 동형(同型)이 된다는 것의 증명(證明)의 개요(槪要)를 소개(紹介)하고 이것을 이용(利用) Rham cohomology ring과 Čech cohomology ring이 동형(同型)임을 증명(證明)한다. 그리고 이 de Rham 이론(理論)이 기하(幾何) 및 해석학(解析學)에 활용(活用)되는 일단(一端)을 기술(記述)하여 볼 예정(豫定)이다.

• 대한수학회보
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• 제57권4호
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• pp.873-890
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• 2020

In this paper, for discrete groups G and K, we show that the cohomology of the complex of projective tensor product B*(G)⨶B*(K) is isomorphic to the bounded cohomology Ĥ*(G × K) of G × K, which is the cohomology of B*(G × K) as topological vector spaces, where B*(G) is a complex of bounded cochains of G with real coefficients ℝ. In fact, we construct an isomorphism between these two cohomology groups that carries the canonical seminorm in Ĥ*(G × K) to the seminorm in the cohomology of B*(G)⨶B*(K).

• 호남수학학술지
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• 제32권2호
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• pp.227-237
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• 2010

For a discrete group G, the kernel of a homomorphism from bounded cohomology $\hat{H}^*(G)$ of G to the ordinary cohomology $H^*(G)$ of G is called the singular part of $\hat{H}^*(G)$. We give some results on the space of the singular part of the second bounded cohomology of G. Also some results on the second bounded cohomology of a uniformly perfect group are given.

• 대한수학회지
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• 제56권6호
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• pp.1655-1687
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• 2019

In this paper we define a new type of cohomology for multiplicative Hom-associative algebras, which generalizes Hom-type Hochschild cohomology and fits with deformations of Hom-associative algebras including the deformation of the structure map ${\alpha}$. Moreover, we provide various observations and similarly a new type cohomology of Hom-bialgebras extending the Gerstenhaber-Schack cohomology for Hom-bialgebras and fitting with formal deformations including deformations of the structure map.

• 대한수학회보
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• 제60권1호
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• pp.149-160
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• 2023

Let 𝖆 and 𝖇 be ideals of a commutative Noetherian ring R and M a finitely generated R-module of finite dimension d > 0. In this paper, we obtain some results about the annihilators and attached primes of top local cohomology and top formal local cohomology modules. In particular, we determine Ann(𝖇 H^d_𝖆(M)), Att(𝖇 H^d_𝖆(M)), Ann(𝖇𝔉^d_𝖆(M)) and Att(𝖇𝔉^d_𝖆(M)).

• 대한수학회지
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• 제59권2호
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• pp.379-405
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• 2022

We introduce the notions of Koszul N-complex, Čech N-complex and telescope N-complex, explicit derived torsion and derived completion functors in the derived category D_N (R) of N-complexes using the Čech N-complex and the telescope N-complex. Moreover, we give an equivalence between the categories of cohomologically 𝖆-torsion N-complexes and cohomologically 𝖆-adic complete N-complexes, and prove that over a commutative Noetherian ring, via Koszul cohomology, via RHom cohomology (resp. ⊗ cohomology) and via local cohomology (resp. derived completion), all yield the same invariant.

• 대한수학회지
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• 제52권4호
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• pp.821-838
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• 2015

We investigate the relative and Tate cohomology theories with respect to Ding modules and complexes, consider their relations with classical and Gorenstein cohomology theories. As an application, the Avramov-Martsinkovsky type exact sequence of Ding modules is obtained.

• 대한수학회지
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• 제57권1호
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• pp.113-129
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• 2020

In this paper, we study the Poisson cohomology ring of the tensor product of Poisson algebras. Explicitly, it is proved that the Poisson cohomology ring of tensor product of two Poisson algebras is isomorphic to the tensor product of the respective Poisson cohomology ring of these two Poisson algebras as Gerstenhaber algebras.

• Kyungpook Mathematical Journal
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• 제63권1호
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• pp.37-43
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• 2023

Let 𝔞 and 𝔟 be ideals of a commutative Noetherian ring R and M be a finitely generated R-module of dimension d > 0. We prove some results concerning the top local cohomology and top formal local cohomology modules. Among other things, we determine Supp_R(𝔟 H^d_𝔞(M)) and Supp_R(𝔟𝔉^d_𝔞(M)). Also, we obtain some relations between Ann_R(𝔟 H^d_𝔞(M)), Att_R(𝔟 H^d_𝔞(M)) and Supp_R(𝔟 H^d_𝔞(M)) and we get similar results for 𝔟𝔉^d_𝔞(M).

• 대한수학회논문집
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• 제11권2호
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• pp.391-405
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• 1996

In this article, we calculate the cohomology groups of flat vector bundles on some manifolds.