• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.401-408
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• 2019

A ring R is called right (resp., left) nilpotent-duo if N(R)a ⊆ aN(R) (resp., aN(R) ⊆ N(R)a) for every a ∈ R, where N(R) is the set of all nilpotents in R. In this article we provide other proofs of known results and other computations for known examples in relation with right nilpotent-duo property. Furthermore we show that the left nilpotent-duo property does not go up to a kind of matrix ring.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.655-663
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• 2014

Let R be a ring with identity, X(R) the set of all nonzero, non-units of R and G(R) the group of all units of R. We show that for a matrix ring $M_n(D)$, $n{\geq}2$, if a, b are singular matrices of the same rank, then ${\mid}o_{\ell}(a){\mid}={\mid}o_{\ell}(b){\mid}$, where $o_{\ell}(a)$ and $o_{\ell}(b)$ are the orbits of a and b, respectively, under the left regular action. We also show that for a semisimple Artinian ring R such that $X(R){\neq}{\emptyset}$, $$R{{\sim_=}}{\oplus}^m_{i=1}M_n_i(D_i)$$, with $D_i$ infinite division rings of the same cardinalities or R is isomorphic to the ring of $2{\times}2$ matrices over a finite field if and only if ${\mid}o_{\ell}(x){\mid}={\mid}o_{\ell}(y){\mid}$ for all $x,y{\in}X(R)$.

• Archives of Pharmacal Research
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• v.5 no.2
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• pp.79-86
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• 1982

Sulfisoxazole, $C-{11}H_{13}N_{3}S$, crystallized in the orthohombic system, space group Pbca, with a = 14.492(1), b = 11.563(1), c = 14.900(2) $\AA$ and Z = 8. Intensities for 1867(1360 observed) unique reflections were measured on a four-circle diffractometer wirh CuKa radiation ($\lambda$ = 1.5418$\AA$). The structure was solved by heavy atom methods and refined by full-matrix least-squares procedures to a final R of 0.094. The benzene ring plane makes an angle of $68^{\circ}C$ with the plane of the isoxazole ring, which is plannar. The conformational angle formed by the torsional angle C(4)-S-N(2)-C(7) is $54^{\circ}C$. There are two intermolecular hydrogen bonds in the structure. One of them is of the type N-H...H with the length 2.915$\AA$. Thus two dimensional networks of hydrogen bonds form infinite moelcular sheets parallel to the (001) plane. Adjacent sheets are bound together by van der Waals forces.