• 제목/요약/키워드: C-M modules

검색결과 135건 처리시간 0.024초

EXTENSIONS OF DRINFELD MODULES OF RANK 2 BY THE CARLITZ MODULE

  • Woo, Sung-Sik
    • 대한수학회보
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    • 제32권2호
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    • pp.251-257
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    • 1995
  • In the catagory of t-modules the Carlitz module C plays the role of $G_m$ in the category of group schemes. For a finite t-module G which corresponds to a finite group scheme, Taguchi [T] showed that Hom (G, C) is the "right" dual in the category of finite- t-modules which corresponds to the Cartier dual of a finite group scheme. In this paper we show that for Drinfeld modules (i.e., t-modules of dimension 1) of rank 2 there is a natural way of defining its dual by using the extension of drinfeld module by the Carlitz module which is in the same vein as defining the dual of an abelian varietiey by its $G_m$-extensions. Our results suggest that the extensions are the right objects to define the dual of arbitrary t-modules.t-modules.

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ON Φ-FLAT MODULES AND Φ-PRÜFER RINGS

  • Zhao, Wei
    • 대한수학회지
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    • 제55권5호
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    • pp.1221-1233
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    • 2018
  • Let R be a commutative ring with non-zero identity and let NN(R) = {I | I is a nonnil ideal of R}. Let M be an R-module and let ${\phi}-tor(M)=\{x{\in}M{\mid}Ix=0\text{ for some }I{\in}NN(R)\}$. If ${\phi}or(M)=M$, then M is called a ${\phi}$-torsion module. An R-module M is said to be ${\phi}$-flat, if $0{\rightarrow}{A{\otimes}_R}\;{M{\rightarrow}B{\otimes}_R}\;{M{\rightarrow}C{\otimes}_R}\;M{\rightarrow}0$ is an exact R-sequence, for any exact sequence of R-modules $0{\rightarrow}A{\rightarrow}B{\rightarrow}C{\rightarrow}0$, where C is ${\phi}$-torsion. In this paper, the concepts of NRD-submodules and NP-submodules are introduced, and the ${\phi}$-flat modules over a ${\phi}-Pr{\ddot{u}}fer$ ring are investigated.

A NOTE ON ENDOMORPHISMS OF LOCAL COHOMOLOGY MODULES

  • Mahmood, Waqas;Zahid, Zohaib
    • 대한수학회보
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    • 제54권1호
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    • pp.319-329
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    • 2017
  • Let I denote an ideal of a Noetherian local ring (R, m). Let M denote a finitely generated R-module. We study the endomorphism ring of the local cohomology module $H^c_I(M)$, c = grade(I, M). In particular there is a natural homomorphism $$Hom_{\hat{R}^I}({\hat{M}}^I,\;{\hat{M}}^I){\rightarrow}Hom_R(H^c_I(M),\;H^c_I(M))$$, $where{\hat{\cdot}}^I$ denotes the I-adic completion functor. We provide sufficient conditions such that it becomes an isomorphism. Moreover, we study a homomorphism of two such endomorphism rings of local cohomology modules for two ideals $J{\subset}I$ with the property grade(I, M) = grade(J, M). Our results extends constructions known in the case of M = R (see e.g. [8], [17], [18]).

On Generalizations of Extending Modules

  • Karabacak, Fatih
    • Kyungpook Mathematical Journal
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    • 제49권3호
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    • pp.557-562
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    • 2009
  • A module M is said to be SIP-extending if the intersection of every pair of direct summands is essential in a direct summand of M. SIP-extending modules are a proper generalization of both SIP-modules and extending modules. Every direct summand of an SIP-module is an SIP-module just as a direct summand of an extending module is extending. While it is known that a direct sum of SIP-extending modules is not necessarily SIP-extending, the question about direct summands of an SIP-extending module to be SIP-extending remains open. In this study, we show that a direct summand of an SIP-extending module inherits this property under some conditions. Some related results are included about $C_{11}$ and SIP-modules.

ON FRAMES FOR COUNTABLY GENERATED HILBERT MODULES OVER LOCALLY C*-ALGEBRAS

  • Alizadeh, Leila;Hassani, Mahmoud
    • 대한수학회논문집
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    • 제33권2호
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    • pp.527-533
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    • 2018
  • Let $\mathcal{X}$ be a countably generated Hilbert module over a locally $C^*$-algebra $\mathcal{A}$ in multiplier module M($\mathcal{X}$) of $\mathcal{X}$. We propose the necessary and sufficient condition such that a sequence $\{h_n:n{{\in}}\mathbb{N}\}$ in M($\mathcal{X}$) is a standard frame of multipliers in $\mathcal{X}$. We also show that if T in $b(L_{\mathcal{A}}(\mathcal{X}))$, the space of bounded maps in set of all adjointable maps on $\mathcal{X}$, is surjective and $\{h_n:n{{\in}}\mathbb{N}\}$ is a standard frame of multipliers in $\mathcal{X}$, then $\{T{\circ}h_n:n{\in}\mathbb{N}}$ is a standard frame of multipliers in $\mathcal{X}$, too.

EXTENSIONS OF t-MODULES

  • Woo, Sung-Sik
    • 대한수학회논문집
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    • 제9권2호
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    • pp.361-367
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    • 1994
  • An elliptic module is an analogue of an elliptic curve over a function field [D]. The dual of an elliptic curve E is represented by Ext(E, $G_{m}$) and the Cartier dual of an affine group scheme G is represented by Hom(G, G$G_{m}$). In the category of elliptic modules the Carlitz module C plays the role of $G_{m}$. Taguchi [T] showed that a notion of duality of a finite t-module can be represented by Hom(G, C) in a suitable category. Our computation shows that the Ext-group as it stands is rather too "big" to represent a dual of an elliptic module.(omitted)

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건물 부착형 고경량 유연성 슁글드 태양광 모듈 (Fabrication of Lightweight Flexible c-Si Shingled Photovoltaic Modules for Building-Applied Photovoltaics)

  • 김민섭;박민준;신진호;이은비;정채환
    • Current Photovoltaic Research
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    • 제10권4호
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    • pp.107-110
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    • 2022
  • Lightweight and flexible photovoltaic (PV) modules are attractive for building-integrated photovoltaic (BIPV) applications because of their easy construction and applicability. In this study, we fabricated lightweight and flexible c-Si PV modules using ethylene tetrafluoroethylene (ETFE) front cover and shingled design string cells. The ETFE front cover instead of glass made the PV modules lighter in weight, and the shingled design string cells increased the flexibility. Finally, we fabricated a PV module with a conversion power of 240.08 W at an area of 1.25 m2 and weighed only 2 kg/m2. Moreover, to check the PV module's flexibility, we conducted a bending test. The difference of conversion power between the modules before and after bending shown was only 1.7 W, which showed a power reduction rate of about 0.7%.