• 제목/요약/키워드: dual modules

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A DECOMPOSITION THEOREM FOR UTUMI AND DUAL-UTUMI MODULES

  • Ibrahim, Yasser;Yousif, Mohamed
    • 대한수학회보
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    • 제58권6호
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    • pp.1563-1567
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    • 2021
  • We show that if M is a Utumi module, in particular if M is quasi-continuous, then M = Q ⊕ K, where Q is quasi-injective that is both a square-full as well as a dual-square-full module, K is a square-free module, and Q & K are orthogonal. Dually, we also show that if M is a dual-Utumi module whose local summands are summands, in particular if M is quasi-discrete, then M = P ⊕ K where P is quasi-projective that is both a square-full as well as a dual-square-full module, K is a dual-square-free module, and P & K are factor-orthogonal.

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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이중구조를 갖는 제어시스템의 구현과 신뢰도 분석에 관한 연구 (A Study on the Implementation of a Control System with Dual Structure and Its Reliability Analysis)

  • 박세화;문봉채;김병국
    • 대한전자공학회논문지
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    • 제27권9호
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    • pp.1351-1363
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    • 1990
  • In this paper, a reliable control system structured with dual CPU modules and dual I/O modules is implemented as a means of achieving a highly reliable fault tolerant control system. For this, faults in the system modules are first examined, and a fault detection technique consisting of self diagnostic, comparison process, and exception processing is applied. Self diagnostic is used to locate which components in the modules have been failed, while comparison process is to cmpare control outputs computed by both CPU modules and protect the plant from malfunction by blocking failed control outputsin advance. Finally exception processing is used to determine the faults that are not detected immediately by the self diagnostic and comparison process, e.g. bus error processing when acknowledge signal for data transfer is not activeted in the I/O modules. Also reliability analysis is conducted for the discrete time Markov model with dual structure. It is shown quantitatively that the reliability is improved in the control system with dual structure in comparison with a system with single module structure.

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ON DUAL ZARISKI TOPOLOGY OVER GRADED COMULTIPLICATION MODULES

  • Abu-Dawwas, Rashid;Alshehry, Azzh Saad
    • 대한수학회논문집
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    • 제36권1호
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    • pp.11-18
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    • 2021
  • In this article, we deal with Zariski topology on graded comultiplication modules. The purpose of this article is obtaining some connections between algebraic properties of graded comultiplication modules and topological properties of dual Zariski topology on graded comultiplication modules.

제어 시스템의 신뢰도 향상을 위한 이중화 구조 연구 (A study on the control system with dual structure to enhance its reliability)

  • 박세화;문봉채;김병국;변증남
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 26-27 Oct. 1990
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    • pp.773-778
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    • 1990
  • In this paper, a reliable control system structured with dual CPU modules and dual I/O modules is implemented as a means of achieving a highly reliable fault tolerant control system. For this, faults in the system modules are first examined, and a fault detection technique consisting of self diagnostic, comparison process, and exception processing is applied. Also reliability analysis is conducted for the discrete time Markov model with dual structure. It is shown quantitatively that the reliability is improved in the control system with dual structure in comparison with a system with single module structure.

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GORENSTEIN WEAK INJECTIVE MODULES WITH RESPECT TO A SEMIDUALIZING BIMODULE

  • Gao, Zenghui;Ma, Xin;Zhao, Tiwei
    • 대한수학회지
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    • 제55권6호
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    • pp.1389-1421
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    • 2018
  • In this paper, we introduce the notion of C-Gorenstein weak injective modules with respect to a semidualizing bimodule $_SC_R$, where R and S are arbitrary associative rings. We show that an iteration of the procedure used to define $G_C$-weak injective modules yields exactly the $G_C$-weak injective modules, and then give the Foxby equivalence in this setting analogous to that of C-Gorenstein injective modules over commutative Noetherian rings. Finally, some applications are given, including weak co-Auslander-Buchweitz context, model structure and dual pair induced by $G_C$-weak injective modules.

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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