• Title, Summary, Keyword: maximal ideal

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FUZZY MAXIMAL P-IDEALS OF BCI-ALGEBRAS

  • JUN, YOUNG BAE;HONG, SUNG MIN
    • Honam Mathematical Journal
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    • v.17 no.1
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    • pp.1-6
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    • 1995
  • Our task will be to set up a fuzzy maximal p-ideal in BCI-algebras. We construct a new fuzzy p-ideal from old. We also prove that every fuzzy maximal p-ideal is normalized, and takes only the values {0.1}.

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Generalizations of V-rings

  • Song, Xianmei;Yin, Xiaobin
    • Kyungpook Mathematical Journal
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    • v.45 no.3
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    • pp.357-362
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    • 2005
  • In this paper, we introduce a new notion which we call a generalized weakly ideal. We also investigate characterizations of strongly regular rings with the condition that every maximal left ideal is a generalized weakly ideal. It is proved that R is a strongly regular ring if and only if R is a left GP-V-ring whose every maximal left (right) ideal is a generalized weakly ideal. Furthermore, if R is a left SGPF ring, and every maximal left (right) ideal is a generalized weakly ideal, it is shown that R/J(R) is strongly regular. Several known results are improved and extended.

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On Rings Containing a Non-essential nil-Injective Maximal Left Ideal

  • Wei, Junchao;Qu, Yinchun
    • Kyungpook Mathematical Journal
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    • v.52 no.2
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    • pp.179-188
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    • 2012
  • We investigate in this paper rings containing a non-essential $nil$-injective maximal left ideal. We show that if R is a left MC2 ring containing a non-essential $nil$-injective maximal left ideal, then R is a left $nil$-injective ring. Using this result, some known results are extended.

ON THE STRUCTURES OF CLASS SEMIGROUPS OF QUADRATIC NON-MAXIMAL ORDERS

  • KIM, YONG TAE
    • Honam Mathematical Journal
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    • v.26 no.3
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    • pp.247-256
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    • 2004
  • Buchmann and Williams[1] proposed a key exchange system making use of the properties of the maximal order of an imaginary quadratic field. $H{\ddot{u}}hnlein$ et al. [6,7] also introduced a cryptosystem with trapdoor decryption in the class group of the non-maximal imaginary quadratic order with prime conductor q. Their common techniques are based on the properties of the invertible ideals of the maximal or non-maximal orders respectively. Kim and Moon [8], however, proposed a key-exchange system and a public-key encryption scheme, based on the class semigroups of imaginary quadratic non-maximal orders. In Kim and Moon[8]'s cryptosystem, a non-invertible ideal is chosen as a generator of key-exchange ststem and their secret key is some characteristic value of the ideal on the basis of Zanardo et al.[9]'s quantity for ideal equivalence. In this paper we propose the methods for finding the non-invertible ideals corresponding to non-primitive quadratic forms and clarify the structure of the class semigroup of non-maximal order as finitely disjoint union of groups with some quantities correctly. And then we correct the misconceptions of Zanardo et al.[9] and analyze Kim and Moon[8]'s cryptosystem.

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ON RINGS CONTAINING A P-INJECTIVE MAXIMAL LEFT IDEAL

  • Kim, Jin-Yong;Kim, Nam-Kyun
    • Communications of the Korean Mathematical Society
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    • v.18 no.4
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    • pp.629-633
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    • 2003
  • We investigate in this paper rings containing a finitely generated p-injective maximal left ideal. We show that if R is a semiprime ring containing a finitely generated p-injective maximal left ideal, then R is a left p-injective ring. Using this result we are able to give a new characterization of von Neumann regular rings with nonzero socle.

KRULL RING WITH UNIQUE REGULAR MAXIMAL IDEAL

  • Chang, Gyu Whan
    • Korean Journal of Mathematics
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    • v.15 no.2
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    • pp.115-119
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    • 2007
  • Let R be a Krull ring with the unique regular maximal ideal M. We show that R has a regular prime element and reg-$dimR=1{\Leftrightarrow}R$ is a factorial ring and reg-$dim(R)=1{\Rightarrow}M$ is invertible ${\Leftrightarrow}R{\varsubsetneq}[R:M]{\Leftrightarrow}M$ is divisorial ${\Leftrightarrow}$ reg-$htM=1{\Rightarrow}R$ is a rank one discrete valuation ring. We also show that if M is generated by regular elements, then R is a rank one discrete valuation ring ${\Rightarrow}$ R is a factorial ring and reg-dim(R)=1.

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The Structure of Maximal Ideal Space of Certain Banach Algebras of Vector-valued Functions

  • Shokri, Abbas Ali;Shokri, Ali
    • Kyungpook Mathematical Journal
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    • v.54 no.2
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    • pp.189-195
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    • 2014
  • Let X be a compact metric space, B be a unital commutative Banach algebra and ${\alpha}{\in}(0,1]$. In this paper, we first define the vector-valued (B-valued) ${\alpha}$-Lipschitz operator algebra $Lip_{\alpha}$ (X, B) and then study its structure and characterize of its maximal ideal space.

The Maximal Ideal Space of Extended Differentiable Lipschitz Algebras

  • Abolfathi, Mohammad Ali;Ebadian, Ali
    • Kyungpook Mathematical Journal
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    • v.60 no.1
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    • pp.117-125
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    • 2020
  • In this paper, we first introduce new classes of Lipschitz algebras of infinitely differentiable functions which are extensions of the standard Lipschitz algebras of infinitely differentiable functions. Then we determine the maximal ideal space of these extended algebras. Finally, we show that if X and K are uniformly regular subsets in the complex plane, then R(X, K) is natural.

DEPTHS OF THE REES ALGEBRAS AND THE ASSOCIATED GRADED RINGS

  • Kim, Mee-Kyoung
    • Bulletin of the Korean Mathematical Society
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    • v.31 no.2
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    • pp.210-214
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    • 1994
  • The purpose of this paper is to investigate the relationship between the depths of the Rees algebra R[It] and the associated graded ring g $r_{I}$(R) of an ideal I in a local ring (R,m) of dim(R) > 0. The relationship between the Cohen-Macaulayness of these two rings has been studied extensively. Let (R, m) be a local ring and I an ideal of R. An ideal J contained in I is called a reduction of I if J $I^{n}$ = $I^{n+1}$ for some integer n.geq.0. A reduction J of I is called a minimal reduction of I. The reduction number of I with respect to J is defined by (Fig.) S. Goto and Y.Shimoda characterized the Cohen-Macaulay property of the Rees algebra of the maximal ideal of a Cohen-Macaulay local ring in terms of the Cohen-Macaulay property of the associated graded ring of the maximal ideal and the reduction number of that maximal ideal. Let us state their theorem.m.m.

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ON r-IDEALS IN INCLINE ALGEBRAS

  • Ahn, Sun-Shin;Kim, Hee-Sik
    • Communications of the Korean Mathematical Society
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    • v.17 no.2
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    • pp.229-235
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    • 2002
  • In this paper we show that if K is an incline with multiplicative identity and I is an r-ideal of k containing a unit u, then I = K. Moreover, we show that in a non-zero incline K with multiplicative identity and zero element, every proper r-ideal in K is contained in a maximal r-ideal of K.