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Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, nil n-injectivity on two extensions of rings are studied. Firstly, it is proved that R∝R is left nil n-injective if and only if r... (lRn(δ) ∩ (Rnδγ) )=δR +γ rR(δ), where δ,γ∈Rn and every component of δ is nilpotent. Secondly, it is proved that, for any α,β∈Rn and every component of α is nilpotent, if every right R-homomorphism from αRn + βrRn (α) to Rcan be extended to an endomorphism of R, then S = R∝R is right nil n-injective. Finally, the following result is obtained: if n ≥ 2, and Tn(R) is right nil n-injective, then R has no nonzero nilpotent elements. « [ABSTRACT FROM AUTHOR]

Let α be an endomorphism of a ring R and αγ = IR for some positive interger γ, it was proved that R is α-skew Armendariz if and only if R[x;α] is Armendariz rings. This is a new connection between Armendarizness and α-skew Armendarizness. [ABSTRACT FROM AUTHOR]