• 제목/요약/키워드: Nilpotent

검색결과 161건 처리시간 0.021초

ON NIL GENERALIZED POWER SERIESWISE ARMENDARIZ RINGS

  • Ouyang, Lunqun;Liu, Jinwang
    • 대한수학회논문집
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    • 제28권3호
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    • pp.463-480
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    • 2013
  • We in this note introduce a concept, so called nil generalized power serieswise Armendariz ring, that is a generalization of both S-Armendariz rings and nil power serieswise Armendariz rings. We first observe the basic properties of nil generalized power serieswise Armendariz rings, constructing typical examples. We next study the relationship between the nilpotent property of R and that of the generalized power series ring [[$R^{S,{\leq}}$]] whenever R is nil generalized power serieswise Armendariz.

A PROPERTY OF P-INJETIVE RING

  • Hong, Chan-Yong
    • 한국수학교육학회지시리즈A:수학교육
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    • 제31권2호
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    • pp.141-144
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    • 1992
  • In this paper, some properties of p-injective ring is studied: The Jacobson radical of a pinjective ring which satisfies the ascending chain condition on essential left ideals is nilpotent. Also, the left singular ideal of a ring which satisfies the ascending chain condition on essential left ideals is nilpotent. Finally, we give an example which shows that a semiprime left p-injective ring such that every essential left ideal is two-sided is not necessarily to be strongly regular.egular.

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GENERALIZED PRIME IDEALS IN NON-ASSOCIATIVE NEAR-RINGS I

  • Cho, Yong-Uk
    • East Asian mathematical journal
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    • 제28권3호
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    • pp.281-285
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    • 2012
  • In this paper, the concept of *-prime ideals in non-associative near-rings is introduced and then will be studied. For this purpose, first we introduce the notions of *-operation, *-prime ideal and *-system in a near-ring. Next, we will define the *-sequence, *-strongly nilpotent *-prime radical of near-rings, and then obtain some characterizations of *-prime ideal and *-prime radical $r_s$(I) of an ideal I of near-ring N.

RINGS IN WHICH NILPOTENT ELEMENTS FORM AN IDEAL

  • Cho, June-Rae;Kim, Nam-Kyun;Lee, Yang
    • East Asian mathematical journal
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    • 제18권1호
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    • pp.15-20
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    • 2002
  • We study the relationships between strongly prime ideals and completely prime ideals, concentrating on the connections among various radicals(prime radical, upper nilradical and generalized nilradical). Given a ring R, consider the condition: (*) nilpotent elements of R form an ideal in R. We show that a ring R satisfies (*) if and only if every minimal strongly prime ideal of R is completely prime if and only if the upper nilradical coincides with the generalized nilradical in R.

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IFP RINGS AND NEAR-IFP RINGS

  • Ham, Kyung-Yuen;Jeon, Young-Cheol;Kang, Jin-Woo;Kim, Nam-Kyun;Lee, Won-Jae;Lee, Yang;Ryu, Sung-Ju;Yang, Hae-Hun
    • 대한수학회지
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    • 제45권3호
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    • pp.727-740
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    • 2008
  • A ring R is called IFP, due to Bell, if ab=0 implies aRb=0 for $a,b{\in}R$. Huh et al. showed that the IFP condition need not be preserved by polynomial ring extensions. But it is shown that ${\sum}^n_{i=0}$ $E_{ai}E$ is a nonzero nilpotent ideal of E whenever R is an IFP ring and $0{\neq}f{\in}F$ is nilpotent, where E is a polynomial ring over R, F is a polynomial ring over E, and $a_i^{'s}$ are the coefficients of f. we shall use the term near IFP to denote such a ring as having place near at the IFPness. In the present note the structures of IFP rings and near-IFP rings are observed, extending the classes of them. IFP rings are NI (i.e., nilpotent elements form an ideal). It is shown that the near-IFPness and the NIness are distinct each other, and the relations among them and related conditions are examined.

ON CONJUGATE POINTS OF THE GROUP H(2, 1)

  • Jang, Chang-Rim;Park, Keun;Lee, Tae-Hoon
    • East Asian mathematical journal
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    • 제22권2호
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    • pp.249-257
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    • 2006
  • Let n be a 2-step nilpotent Lie algebra which has an inner product <,> and has an orthogonal decomposition $n=\delta{\oplus}\varsigma$ for its center $\delta$ and the orthogonal complement $\varsigma\;of\;\delta$. Then Each element Z of $\delta$ defines a skew symmetric linear map $J_Z:\varsigma{\rightarrow}\varsigma$ given by $=$ for all $X,\;Y{\in}\varsigma$. Let $\gamma$ be a unit speed geodesic in a 2-step nilpotent Lie group H(2, 1) with its Lie algebra n(2, 1) and let its initial velocity ${\gamma}$(0) be given by ${\gamma}(0)=Z_0+X_0{\in}\delta{\oplus}\varsigma=n(2,\;1)$ with its center component $Z_0$ nonzero. Then we showed that $\gamma(0)$ is conjugate to $\gamma(\frac{2n{\pi}}{\theta})$, where n is a nonzero intger and $-{\theta}^2$ is a nonzero eigenvalue of $J^2_{Z_0}$, along $\gamma$ if and only if either $X_0$ is an eigenvector of $J^2_{Z_0}$ or $adX_0:\varsigma{\rightarrow}\delta$ is not surjective.

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