• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.223-234
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• 2003

This note contains the following results for a ring A : (1) A is simple Artinian if and only if A is a prime right YJ-injective, right and left V-ring with a maximal right annihilator ; (2) if A is a left quasi-duo ring with Jacobson radical J such that $_{A}$A/J is p-injective, then the ring A/J is strongly regular ; (3) A is von Neumann regular with non-zero socle if and only if A is a left p.p.ring containing a finitely generated p-injective maximal left ideal satisfying the following condition : if e is an idempotent in A, then eA is a minimal right ideal if and only if Ae is a minimal left ideal ; (4) If A is left non-singular, left YJ-injective such that each maximal left ideal of A is either injective or a two-sided ideal of A, then A is either left self-injective regular or strongly regular : (5) A is left continuous regular if and only if A is right p-injective such that for every cyclic left A-module M, $_{A}$M/Z(M) is projective. ((5) remains valid if 《continuous》 is replaced by 《self-injective》 and 《cyclic》 is replaced by 《finitely generated》. Finally, we have the following two equivalent properties for A to be von Neumann regula. : (a) A is left non-singular such that every finitely generated left ideal is the left annihilator of an element of A and every principal right ideal of A is the right annihilator of an element of A ; (b) Change 《left non-singular》 into 《right non-singular》in (a).(a).

• Bulletin of the Korean Chemical Society
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• v.33 no.6
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• pp.1861-1866
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• 2012

The new semiconducting copolymers with 4,4-dialkyl-$4H$-cyclopenta[2,1-$b$:3,4-$b^{\prime}$]dithiophene and 2,2-dimethyl-$2H$-benzimidazole units were synthesized. The fused aromatic rings, such as cyclopentadithiophene (CPDT) unit, can make the polymer backbone more rigid and coplanar, which induces long conjugation length, narrow band gap, and strong intermolecular ${\pi}-{\pi}$ interaction. The stacking ability was controlled through attaching of linear or branched alkyl side chains. The spectra of PEHCPDTMBI and PHCPDTMBI in the solid films show absorption bands with maximum peaks at 401, 759 and 407, 768 nm, and the absorption onsets at 925 and 954 nm, corresponding to band gaps of 1.34 and 1.30 eV, respectively. The devices comprising PHCPDTMBI with $TiO_X$ showed a $V_{OC}$ of 0.39 V, a $J_{SC}$ of 1.14 $mA/cm^2$, and a $FF$ of 0.34, giving a power conversion efficiency of 0.15%. The PHCPDTMBI with linear alkyl chain on CPDT shows good solubility in organic solvent with higher PCE value than that of PEHCPDTMBI.