• Title/Summary/Keyword: lifting module

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ON THE DECOMPOSITION OF EXTENDING LIFTING MODULES

  • Chang, Chae-Hoon;Shin, Jong-Moon
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.6
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    • pp.1069-1077
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    • 2009
  • In 1984, Oshiro [11] has studied the decomposition of continuous lifting modules. He obtained the following: every continuous lifting module has an indecomposable decomposition. In this paper, we study extending lifting modules. We show that every extending lifting module has an indecomposable decomposition. This result is an expansion of Oshiro's result mentioned above. And we consider some application of this result.

On Lifting Modules and Weak Lifting Modules

  • Tutuncu, Derya Keskin;Tribak, Rachid
    • Kyungpook Mathematical Journal
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    • v.45 no.3
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    • pp.445-453
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    • 2005
  • We say that a module M is weak lifting if M is supplemented and every supplement submodule of M is a direct summand. The module M is called lifting, if it is weak lifting and amply supplemented. This paper investigates the structure of weak lifting modules and lifting modules having small radical over commutative noetherian rings.

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X-LIFTING MODULES OVER RIGHT PERFECT RINGS

  • Chang, Chae-Hoon
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.1
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    • pp.59-66
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    • 2008
  • Keskin and Harmanci defined the family B(M,X) = ${A{\leq}M|{\exists}Y{\leq}X,{\exists}f{\in}Hom_R(M,X/Y),\;Ker\;f/A{\ll}M/A}$. And Orhan and Keskin generalized projective modules via the class B(M, X). In this note we introduce X-local summands and X-hollow modules via the class B(M, X). Let R be a right perfect ring and let M be an X-lifting module. We prove that if every co-closed submodule of any projective module P contains Rad(P), then M has an indecomposable decomposition. This result is a generalization of Kuratomi and Chang's result [9, Theorem 3.4]. Let X be an R-module. We also prove that for an X-hollow module H such that every non-zero direct summand K of H with $K{\in}B$(H, X), if $H{\oplus}H$ has the internal exchange property, then H has a local endomorphism ring.

On Direct Sums of Lifting Modules and Internal Exchange Property

  • Dejun, Wu
    • Kyungpook Mathematical Journal
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    • v.46 no.1
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    • pp.11-18
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    • 2006
  • Let R be a ring with identity and let $M=M_1{\bigoplus}M_2$ be an amply supplemented R-module. Then it is proved that $M_i$ has ($D_1$) and is $M_j-^*ojective$ for $i{\neq}j$, i = 1, 2, if and only if for any coclosed submodule X of M, there exist $M\acute{_1}{\leq}M_1$ and $M\acute{_2}{\leq}M_2$ such that $M=X{\bigoplus}M\acute{_1}{\bigoplus}M\acute{_2}$.

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Modules Which Are Lifting Relative To Module Classes

  • Kosan, Muhammet Tamer;Harmanci, Abdullah
    • Kyungpook Mathematical Journal
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    • v.48 no.1
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    • pp.63-71
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    • 2008
  • In this paper, we study a module which is lifting and supplemented relative to a module class. Let R be a ring, and let X be a class of R-modules. We will define X-lifting modules and X-supplemented modules. Several properties of these modules are proved. We also obtain results for the case of specific classes of modules.

Finitely Generated Modules over Semilocal Rings and Characterizations of (Semi-)Perfect Rings

  • Chang, Chae-Hoon
    • Kyungpook Mathematical Journal
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    • v.48 no.1
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    • pp.143-154
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    • 2008
  • Lomp [9] has studied finitely generated projective modules over semilocal rings. He obtained the following: finitely generated projective modules over semilocal rings are semilocal. We shall give necessary and sufficient conditions for finitely generated modules to be semilocal modules. By using a lifting property, we also give characterizations of right perfect (semiperfect) rings. Our main results can be summarized as follows: (1) Let M be a finitely generated module. Then M has finite hollow dimension if and only if M is weakly supplemented if and only if M is semilocal. (2) A ring R is right perfect if and only if every flat right R-module is lifting and every right R-module has a flat cover if and only if every quasi-projective right R-module is lifting. (3) A ring R is semiperfect if and only if every finitely generated flat right R-module is lifting if and only if RR satisfies the lifting property for simple factor modules.

Development of a Shower Carrier based on the Needs in Long-term Care Institutions

  • Cho, Deok-Yeon;Ko, Cheol-Woong;Chun, Keyoung-Jin;No, Kon-Woo
    • Journal of the Ergonomics Society of Korea
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    • v.31 no.2
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    • pp.379-388
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    • 2012
  • Objective: This study developed a new shower carrier prototype to reduce caregivers' muscle burden and to increase use convenience by reflecting the needs of domestic long-term care institutions. Background: In the long-term care institutions, one of the ADL(Activities of Daily Life) factors is bathing/showering. Recently, bath/shower-assisting equipment is actively being introduced in care institutions to reduce the caregivers' care cost, but most of the domestic equipment was designed to imitate foreign products and rarely reflected the needs of care institutions. Method: Based on Korean elderly people's body information, the bed size(length: 1,900mm, width: 650mm) was set-up, and a variable headrest with a newly designed headform was developed to provide the comfort for the elderly and convenience for caregivers. To reduce caregivers' muscle burden on transferring and showering activities, a 3-step column lifting module equipped with dual actuators(lowest/highest levels from the ground: 600/1,100mm, Stroke: 500mm) was developed, and the wheelbase parameter(length: 1,250mm, width: 580mm) was defined securing the turn-over safety of the shower carrier. The drivability tests were performed for the prototype and foreign product, and the male and female subject's muscle activities were measured through the tests. Results: The structural stability of the shower carrier prototype was secured by finite element analysis, and the muscle activities of the subjects through the drivability tests largely decreased in the prototype, compared to the foreign product. Conclusion: In this study, a new shower carrier prototype was developed to possibly reduce caregivers' muscle burden and to increase use convenience based on the needs of long-term care institutions. It was expected that the drivability performance of the prototype could be relatively superior to that of the foreign product. Application: The results obtained from the study can be applied for the optimal development of a shower carrier including other equipment to effectively care for the elderly.

Cooperative control system of the floating cranes for the dual lifting

  • Nam, Mihee;Kim, Jinbeom;Lee, Jaechang;Kim, Daekyung;Lee, Donghyuk;Lee, Jangmyung
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.10 no.1
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    • pp.95-102
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    • 2018
  • This paper proposes a dual lifting and its cooperative control system with two different kinds of floating cranes. The Mega-erection and Giga-erection in the ship building are used to handle heavier and wider blocks and modules as ships and off-shore platforms are enlarged. However, there is no equipment to handle such Tera-blocks. In order to overcome the limit on performance of existing floating cranes, the dual lifting is proposed in this research. In the dual lifting, two floating cranes are well-coordinated to add up the lift capabilities of both cranes without any loss such that virtually a single crane is lifting, maneuvering and unloading. Two main constraints for the dual lifting are as follows: First, two barges of floating cranes should be constrained as a rigid body not to cause a relative motion between two barges and main hooks of the two cranes should be controlled as main hooks of a single crane. In order words, it is necessary to develop the cooperative control of two floating cranes in order to sustain a center of gravity of the module and minimize the tilting angle during the lifting and unloading by the two floating cranes. Two floating cranes are handled as a master-slave system. The master crane is able to gather information about all working conditions and make a decision to control the individual hook speed, which communicates the slave crane by TCP/IP. The developed control system has been embedded in the real floating crane systems and the dual lifting has been demonstrated five times at SHI shipyard in 2015. The moving angles of the lifting module are analyzed and verified to be suitable for hoisting control. It is verified that the dual lifting can be applied for many heavier and wider blocks and modules to shorten the construction time of ships and off-shore platforms.