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Let $R$ be a ring. It is well-known that $R$ is {\it NI} if and only if $\sum_{i=0}^nRa_iR$ is a nil ideal of $R$ whenever a polynomial $\sum_{i=0}^na_ix^i$ is nilpotent, where $x$ is an indeterminate over $R$. We consider a condition which is similar to the preceding one: $\sum_{i=0}^nRa_iR$ contains a nonzero nil ideal of $R$ whenever $\sum_{i=0}^na_ix^i$ over $R$ is nilpotent. A ring will be said to be {\it quasi-NI} if it satisfies this condition. The structure of quasi-NI rings is observed, and various examples are given to situations which raised naturally in the process.
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참고문헌 (13)
참고문헌 신청
G.F. Birkenmeier / 1994 / A connection between weak regularity and the simplicity of prime factor rings / Proc. Amer. Math. Soc 122:53~58
J.L. Dorroh / 1932 / Concerning adjunctins to algebras / Bull. Amer. Math. Soc 38:85~88
K. R. Goodearl / 1979 / Von Neumann Regular Rings / Pitman
D. Handelman / 1975 / Strongly prime rings / Tran. Amer. Math. Soc 211:209~223
C.Y. Hong / 2000 / On minimal strongly prime ideals / Comm. Algebra 28:4867~4878
J.L. Dorroh / 1932 / Concerning adjunctins to algebras / Bull. Amer. Math. Soc 38:85~88
K. R. Goodearl / 1979 / Von Neumann Regular Rings / Pitman
D. Handelman / 1975 / Strongly prime rings / Tran. Amer. Math. Soc 211:209~223
C.Y. Hong / 2000 / On minimal strongly prime ideals / Comm. Algebra 28:4867~4878
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