• Title/Summary/Keyword: D-R

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DERIVATION MODULES OF GROUP RINGS AND INTEGERS OF CYCLOTOMIC FIELDS

  • Chung, I.Y.
    • Bulletin of the Korean Mathematical Society
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    • v.20 no.1
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    • pp.31-36
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    • 1983

  • Let R be a commutative ring with 1, and A a unitary commutative R-algebra. By a derivation module of A, we mean a pair (M, d), where M is an A-module and d: A.rarw.M and R-derivation, i.e., d is an R-linear mapping such that d(ab)=a)db)+b(da). A derivation module homomorphism f:(M,d).rarw.(N, .delta.) is an A-homomorphism f:M.rarw.N such that f.d=.delta.. A derivation module of A, (U, d), there exists a unique derivation module homomorphism f:(U, d).rarw.(M,.delta.). In fact, a universal derivation module of A exists in the category of derivation modules of A, and is unique up to unique derivation module isomorphisms [2, pp. 101]. When (U,d) is a universal derivation module of R-algebra A, the A-module U is denoted by U(A/R). For out convenience, U(A/R) will also be called a universal derivation module of A, and d the R-derivation corresponding to U(A/R).

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STABILITY OF THE BERGMAN KERNEL FUNCTION ON PSEUDOCONVEX DOMAINS IN $C^n$

  • Cho, Hong-Rae
    • Communications of the Korean Mathematical Society
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    • v.10 no.2
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    • pp.349-355
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    • 1995

  • Let $D \subset C^n$ be a smoothly bounded pseudoconvex domain and let ${\bar{D}_r}_r$ be a family of smooth perturbations of $\bar{D}$ such that $\bar{D} \subset \bar{D}_r$. Let $K_D(z, w)$ be the Bergman kernel function on $D \times D$. Then $lim_{r \to 0} K_{D_r}(z, w) = K_D(z, w)$ locally uniformally on $D \times D$.

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EAKIN-NAGATA THEOREM FOR COMMUTATIVE RINGS WHOSE REGULAR IDEALS ARE FINITELY GENERATED

  • Chang, Gyu Whan
    • Korean Journal of Mathematics
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    • v.18 no.3
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    • pp.271-275
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    • 2010

  • Let R be a commutative ring with identity, T(R) be the total quotient ring of R, and D be a ring such that $R{\subseteq}D{\subseteq}T(R)$ and D is a finite R-module. In this paper, we show that each regular ideal of R is finitely generated if and only if each regular ideal of D is finitely generated. This is a generalization of the Eakin-Nagata theorem that R is Noetherian if and only if D is Noetherian.

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R&D Funding and R&D Performance : The Moderating Effect of Indirect R&D Cost Ratio (연구비 재원과 연구개발성과 : 간접비 비율의 조절효과를 중심으로)

  • Lee, Joonbeom
    • Journal of Korea Technology Innovation Society
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    • v.21 no.1
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    • pp.420-453
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    • 2018

  • In the growth of the government's investment in national R&D project and the abuse of research expense, an effective control and management mechanism is strongly demanded. However, an excessive regulation might hinder the R&D performance, which also endangers the underlying objective of R&D policy. Especially, an excessive regulation on the R&D expenditure may damage the SMEs (Small and Medium sized Enterprises) where securing an adequate level of R&D funding is vital. This study investigates the R&D funding and R&D performance of SMEs participating in the national R&D project by using fixed effect panel model. As a result, this paper reveals the effectiveness of 'Government R&D subsidy'. However, that of 'private R&D fund' is not supported strongly. Also, this paper empirically demonstrates the efficiency of both 'Government R&D subsidy' and 'Private R&D fund' as the R&D costs are spent discretionarily (as the degree of 'Indirect Cost Ratio' increases). Especially, the effectiveness of 'Private R&D fund' can be moderated by 'Indirect Cost Ratio'. On the basis of the conclusions, this paper draws an implication that can increase R&D performance of SMEs through the interactions of manifold administrative values (i.e. effectiveness, efficiency and responsibility).

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