• Title, Summary, Keyword: regular element

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A special decomposition of regular *-semigroups

  • Shin, Jong-Moon
    • Communications of the Korean Mathematical Society
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    • v.10 no.3
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    • pp.603-607
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    • 1995
  • This paper gives some basic properties on a disjoint decomposition of regular *-semigroups and shows thata regular *-semigroup with a left magnifying element has an identity element.

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CHARACTERIZATIONS OF SOME CLASSES OF $\Gamma$-SEMIGROUPS

  • Kwon, Young-In
    • East Asian mathematical journal
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    • v.14 no.2
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    • pp.393-397
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    • 1998
  • The author obtains ideal-theoretical characterizations of the following two classes of $\Gamma$-semigroups; (1) regular $\Gamma$-semigroups; (2) $\Gamma$-semigroups that are both regular and intra-regular.

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THE STRUCTURE OF ALMOST REGULAR SEMIGROUPS

  • Chae, Younki;Lim, Yongdo
    • Bulletin of the Korean Mathematical Society
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    • v.31 no.2
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    • pp.187-192
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    • 1994
  • The author extended the small properties of topological semilattices to that of regular semigroups [3]. In this paper, it could be shown that a semigroup S is almost regular if and only if over bar RL = over bar R.cap.L for every right ideal R and every left ideal L of S. Moreover, it has shown that the Bohr compactification of an almost regular semigroup is regular. Throughout, a semigroup will mean a topological semigroup which is a Hausdorff space together with a continuous associative multiplication. For a semigroup S, we denote E(S) by the set of all idempotents of S. An element x of a semigroup S is called regular if and only if x .mem. xSx. A semigroup S is termed regular if every element of S is regular. If x .mem. S is regular, then there exists an element y .mem S such that x xyx and y = yxy (y is called an inverse of x) If y is an inverse of x, then xy and yx are both idempotents but are not always equal. A semigroup S is termed recurrent( or almost pointwise periodic) at x .mem. S if and only if for any open set U about x, there is an integer p > 1 such that x$^{p}$ .mem.U.S is said to be recurrent (or almost periodic) if and only if S is recurrent at every x .mem. S. It is known that if x .mem. S is recurrent and .GAMMA.(x)=over bar {x,x$^{2}$,..,} is compact, then .GAMMA.(x) is a subgroup of S and hence x is a regular element of S.

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On Semirings which are Distributive Lattices of Rings

  • Maity, S.K.
    • Kyungpook Mathematical Journal
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    • v.45 no.1
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    • pp.21-31
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    • 2005
  • We introduce the notions of nilpotent element, quasi-regular element in a semiring which is a distributive lattice of rings. The concept of Jacobson radical is introduced for this kind of semirings.

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G-REGULAR SEMIGROUPS

  • Sohn, Mun-Gu;Kim, Ju-Pil
    • Bulletin of the Korean Mathematical Society
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    • v.25 no.2
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    • pp.203-209
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    • 1988
  • In this paper, we define a g-regular semigroup which is a generalization of a regular semigroup. And we want to find some properties of g-regular semigroup. G-regular semigroups contains the variety of all regular semigroup and the variety of all periodic semigroup. If a is an element of a semigroup S, the smallest left ideal containing a is Sa.cup.{a}, which we may conveniently write as $S^{I}$a, and which we shall call the principal left ideal generated by a. An equivalence relation l on S is then defined by the rule alb if and only if a and b generate the same principal left ideal, i.e. if and only if $S^{I}$a= $S^{I}$b. Similarly, we can define the relation R. The equivalence relation D is R.L and the principal two sided ideal generated by an element a of S is $S^{1}$a $S^{1}$. We write aqb if $S^{1}$a $S^{1}$= $S^{1}$b $S^{1}$, i.e. if there exist x,y,u,v in $S^{1}$ for which xay=b, ubv=a. It is immediate that D.contnd.q. A semigroup S is called periodic if all its elements are of finite order. A finite semigroup is necessarily periodic semigroup. It is well known that in a periodic semigroup, D=q. An element a of a semigroup S is called regular if there exists x in S such that axa=a. The semigroup S is called regular if all its elements are regular. The following is the property of D-classes of regular semigroup.group.

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ON COMMUTATIVITY OF REGULAR PRODUCTS

  • Kwak, Tai Keun;Lee, Yang;Seo, Yeonsook
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1713-1726
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    • 2018
  • We study the one-sided regularity of matrices in upper triangular matrix rings in relation with the structure of diagonal entries. We next consider a ring theoretic condition that ab being regular implies ba being also regular for elements a, b in a given ring. Rings with such a condition are said to be commutative at regular product (simply, CRP rings). CRP rings are shown to be contained in the class of directly finite rings, and we prove that if R is a directly finite ring that satisfies the descending chain condition for principal right ideals or principal left ideals, then R is CRP. We obtain in particular that the upper triangular matrix rings over commutative rings are CRP.

Rings which satisfy the Property of Inserting Regular Elements at Zero Products

  • Kim, Hong Kee;Kwak, Tai Keun;Lee, Yang;Seo, Yeonsook
    • Kyungpook Mathematical Journal
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    • v.60 no.2
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    • pp.307-318
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    • 2020
  • This article concerns the class of rings which satisfy the property of inserting regular elements at zero products, and rings with such property are called regular-IFP. We study the structure of regular-IFP rings in relation to various ring properties that play roles in noncommutative ring theory. We investigate conditions under which the regular-IFPness pass to polynomial rings, and equivalent conditions to the regular-IFPness.

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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A KIND OF NORMALITY RELATED TO REGULAR ELEMENTS

  • Huang, Juan;Piao, Zhelin
    • Honam Mathematical Journal
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    • v.42 no.1
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    • pp.93-103
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    • 2020
  • This article concerns a property of Abelain π-regular rings. A ring R shall be called right quasi-DR if for every a ∈ R there exists n ≥ 1 such that C(R)an ⊆ aR, where C(R) means the monoid of regular elements in R. The relations between the right quasi-DR property and near ring theoretic properties are investigated. We next show that the class of right quasi-DR rings is quite large.

Formulation of an Interface Element and Stiffness Evaluation of an Leaf Spring (계면 요소의 구성과 이를 이용한 겹판스프링의 강성도 평가)

  • 정정희;임장근
    • Transactions of the Korean Society of Automotive Engineers
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    • v.5 no.6
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    • pp.141-147
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    • 1997
  • For the effective finite element analysis of the structures including material interfaces or contact surfaces, interface elements are proposed. Most of early works in this problem require not only iterative computation but also complex formulation because of the kinematic nonlinearities caused from the discontinuous behavior and the stress concentration phenomena. The proposed elements, however, are consistently formulated using relative displacements and tractions between top and bottom regular finite elements. The effectiveness of these elements are shown by solving various numerical sample problems including an leaf spring and comparing with results of general finite element analysis. As a result, more stable solutions are conveniently obtaines using interface elements than regular finite elements.

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