• The Pure and Applied Mathematics
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• v.6 no.1
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• pp.9-12
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• 1999

The purpose of this paper is to show that by the divisibility of a direct injective module, we obtain some results with respect to a direct injective module.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.679-687
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• 2005

In this paper we shall give a new definition for a quasi-power module P(M) and discuss some properties for P(M). The quasi-power module P(M) is a direct sum of invertible quasi-submodules C(H)'s of P(M) and then the quasi-submodule C(H) is also a direct sum of strongly cyclic quasi-submodules of C(H). When M is a quasi-perfect right R-module, we shall see that the quasi-power module P(M) is invertible.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.673-682
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• 2020

For the recently defined notion of strongly lifting modules, it has been shown that a direct sum is not, in general, strongly lifting. In this paper we investigate the question: When are the direct sums of strongly lifting modules, also strongly lifting? We introduce the notion of a relatively strongly projective module and use it to show if M = M1 ⊕ M2 is amply supplemented, then M is strongly lifting if and only if M1 and M2 are relatively strongly projective and strongly lifting. Also, we consider when an arbitrary direct sum of hollow (resp. local) modules is strongly lifting.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.173-180
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• 1994

Let H be a separable, infinite dimensional, compled Hilbert space and let L(H) be the algebra of all bounded linear operators on H. A dual algebra is a subalgebra of L(H) that contains the identity operator $I_{H}$ and is closed in the ultraweak topology on L(H). Note that the ultraweak operator topology coincides with the wea $k^{*}$ topology on L(H)(see [3]). Bercovici-Foias-Pearcy [3] studied the problem of solving systems of simultaneous equations in the predual of a dual algebra. The theory of dual algebras has been applied to the topics of invariant subspaces, dilation theory and reflexibity (see [1],[2],[3],[5],[6]), and is deeply related with properties ( $A_{m,n}$). Jung-Lee-Lee [7] introduced n-separating sets for subalgebras and proved the relationship between n-separating sets and properties ( $A_{m,n}$). In this paper we will study the relationship between direct sum and properties ( $A_{m,n}$). In particular, using some results of [7] we obtain relationship between n-separating sets and direct sum of von Neumann algebras.ras.s.ras.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.667-679
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• 2007

We study the prime ideal structure of the direct sum of directed system of rings indexed by a commutative semigroup which is nilpotent extension of a group.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.531-538
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• 2019

We introduce FI-${\oplus}$-supplemented modules as a proper generalization of ${\oplus}$-supplemented modules. We prove that; (1) every finite direct sum of FI-${\oplus}$-supplemented R-modules is an FI-${\oplus}$-supplemented R-module for any ring R ; (2) if every left R-module is FI-${\oplus}$-supplemented over a semilocal ring R, then R is left perfect; (3) if M is a finitely generated torsion-free uniform R-module over a commutative integrally closed domain such that every direct summand of M is FI-${\oplus}$-supplemented, then M is a direct sum of cyclic modules.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.5
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• pp.1944-1956
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• 2021

This paper considers a cellular two-way relay network with one base station (BS), one relay station (RS), and two users. The two users are far from the BS and no direct links exist, and the two users exchange messages with the BS via the RS. A non-orthogonal multiple access (NOMA) and network coding (NC)-based decode-and-forward (DF) two-way relaying (TWR) scheme TWR-NOMA-NC is proposed, which is able to reduce the number of channel-uses to three from four in conventional time-division multiple access (TDMA) based TWR approaches. The achievable sum-rate performance of the proposed approach is analyzed, and a closed-form expression for the sum-rate upper bound is derived. Numerical results show that the analytical sum-rate upper bound is tight, and the proposed TWR-NOMA-NC scheme significantly outperforms the TDMA-based TWR and NOMA-based one-way relaying counterparts.

• Journal of the Korean Mathematical Society
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• v.10 no.1
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• pp.1-7
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• 1973

• Kyungpook Mathematical Journal
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• v.32 no.3_spc
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• pp.517-522
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• 1992

• Journal of Broadcast Engineering
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• v.10 no.3
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• pp.321-327
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• 2005

A MVC (Multi-view Video Coding) method, which uses both an illumination change-adaptive ME (Motion Estimation)/DC (Motion Compensation) and a 2D (Dimensional) direct mode, is proposed. Firstly, a new SAD (Sum of Absolute Difference) measure for ME/MC is proposed to compensate the Luma pixel value changes for spatio-temporal motion vector prediction. Illumination change-adaptive (ICA) ME/MC uses the new SAD to improve both MV (Motion Vector) accuracy and bit saving. Secondly, The proposed 2D direct mode that can be used in inter-view prediction is an extended version of the temporal direct mode in MPEG-4 AVC. The proposed MVC method obtains approximately 0.8dB PSNR (Peak Signal-to-Noise Ratio) increment compared with the MPEG-4 AVC simulcast coding.