• 대한수학회보
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• 제38권4호
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• pp.787-795
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• 2001

For the generalized nilpotent spaces, e.g. the locally nilpotent space, the residually locally nilpotent space and the space satisfying the condition ($T^{*}$) or ($T^{**}$), we find the pullback property of them. Furthermore we investigate some fiber properties of the space satisfying the condition ($T^{*}$) or ($T^{**}$), especially locally nilpotent space.

• 대한수학회논문집
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• 제33권4호
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• pp.1103-1112
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• 2018

We study the structure of a generalization of right nilpotent-duo rings in relation with powers of elements. Such a ring property is said to be weakly right nilpotent-duo. We find connections between weakly right nilpotent-duo and weakly right duo rings, in several algebraic situations which have roles in ring theory. We also observe properties of weakly right nilpotent-duo rings in relation with their subrings and extensions.

• East Asian mathematical journal
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• 제29권3호
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• pp.349-353
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• 2013

In this paper, we study equations over nilpotent groups of class 2. We show that there are some overgroups which contains solutions of equations with exponent sum 1 over nilpotent groups of class 2. As known, equations over a field has a solution in an extension field which contains a copy of the given field. But it is not easy to find that a solution of equations over groups. In many cases, even if equations over groups has a solution, the overgroup is not concrete but very Here we find the concrete overgroups in case of nilpotent groups.

• East Asian mathematical journal
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• 제26권5호
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• pp.607-614
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• 2010

In this paper, we obtain geodesic formula of a certain class of Pseudoriemmanian 2-step nilpotent groups and show a constancy of represenation matrix of Jacobi oprerators along geodesics in Pseudoriemmanian 2-step nilpotent groups with one dimensional center.

• 충청수학회지
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• 제32권4호
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• pp.401-408
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• 2019

A ring R is called right (resp., left) nilpotent-duo if N(R)a ⊆ aN(R) (resp., aN(R) ⊆ N(R)a) for every a ∈ R, where N(R) is the set of all nilpotents in R. In this article we provide other proofs of known results and other computations for known examples in relation with right nilpotent-duo property. Furthermore we show that the left nilpotent-duo property does not go up to a kind of matrix ring.

• 대한수학회지
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• 제43권3호
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• pp.539-552
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• 2006

For an $n{\times}n$ Boolean matrix A, A is called nilpotent if $A^m=O$ for some positive integer m. We consider the set of $n{\times}n$ nilpotent Boolean matrices and we characterize linear operators that strongly preserve nilpotent matrices over Boolean algebras.

• Korean Journal of Mathematics
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• 제6권2호
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• pp.137-148
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• 1998

We briefly discuss the Lie groups, it's nilpotency and representations of a nilpotent Lie groups. Dixmier and Kirillov proved that simply connected nilpotent Lie groups over $\mathbb{R}$ are monomial. We reformulate the above result at the Lie algebra level.

• 대한수학회보
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• 제58권1호
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• pp.47-58
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• 2021

In this article, we completely determine the rings for which every element is a sum of a nilpotent and three tripotents that commute with one another. We discuss this property for some extensions of rings, including group rings.

• 대한수학회지
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• 제55권5호
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• pp.1257-1268
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• 2018

In this article we first investigate a sort of unit-IFP ring by which Antoine provides very useful information to ring theory in relation with the structure of coefficients of zero-dividing polynomials. Here we are concerned with the whole shape of units and nilpotent elements in such rings. Next we study the properties of unit-IFP rings through group actions of units on nonzero nilpotent elements. We prove that if R is a unit-IFP ring such that there are finite number of orbits under the left (resp., right) action of units on nonzero nilpotent elements, then R satisfies the descending chain condition for nil left (resp., right) ideals of R and the upper nilradical of R is nilpotent.

• 대한수학회논문집
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• 제25권1호
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• pp.11-18
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• 2010

The work in this paper was motivated by [3], where Eschenbach and Li listed four 4 by 4 sign patterns, conjectured to be nilpotent sign patterns of nilpotence index at least 3. These sign patterns with no zero entries, called full sign patterns, are shown to be potentially nilpotent of nilpotence index 3. We also generalize these sign patterns of order 4 so that we provide classes of n by n sign patterns of nilpotence indices at least 3, if they are potentially nilpotent. Furthermore it is shown that if a full sign pattern A of order n has nilpotence index k with $2{\leq}k{\leq}n-1$, then sign pattern A has nilpotent realizations of nilpotence indices k, k + 1, $\ldots$, n. Hence, the four 4 by 4 sign patterns in [3, page 91] also allow nilpotent realizations of nilpotence index 4.