• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.183-193
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• 2021

In this paper, we prove that there is a bijection between the ��-tilting modules and the sincere left finite semibricks. We also construct (sincere) semibricks over split-by-nilpotent extensions. More precisely, let �� be a split-by-nilpotent extension of a finite-dimensional algebra �� by a nilpotent bimodule ��E��, and �� ⊆ mod ��. We prove that �� ⊗�� �� is a (sincere) semibrick in mod �� if and only if �� is a semibrick in mod �� and Hom��(��, �� ⊗�� E) = 0 (and �� ∪ �� ⊗�� E is sincere). As an application, we can construct ��-tilting modules and support ��-tilting modules over ��-tilting finite cluster-tilted algebras.

• East Asian mathematical journal
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• v.34 no.1
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• pp.39-46
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• 2018

In this article we consider rings whose Jacobson radical contains all the nilpotent elements, and call such a ring an NJ-ring. The class of NJ-rings contains NI-rings and one-sided quasi-duo rings. We also prove that the Koethe conjecture holds if and only if the polynomial ring R[x] is NJ for every NI-ring R.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.779-783
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• 2004

A group G is said to satisfy the minimal condition on normal subgroups of infinite index if there does not exist an infinite properly descending chain $G_1$ > $G_2$ > ... of normal subgroups of infinite index in G. We characterize the structure of locally nilpotent groups satisfying this chain condition.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.653-666
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• 2020

In this paper, when G is a connected and simply connected nilpotent Lie group of dimension less than or equal to four, we study the uniform lattices Γ of G up to isomorphism and then we study the structure of the automorphism group Aut(Γ) of Γ from the viewpoint of splitting as a natural extension.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.635-644
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• 2006

For a lower niltriangular matrix ring $A=NT_n(K)(n{\geq}3)$, we show that every derivation of A is a sum of certain diagonal, trivial extension and strongly nilpotent derivation. Moreover, a strongly nilpotent derivation is a sum of an inner derivation and an uaz-derivation.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.53-64
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• 2006

In this paper, we are concerned with the algebraic representation of the quasi-nilpotent part for prehermitian operators on Banach spaces. The quasi-nilpotent part of an operator plays a significant role in the spectral theory and Fredholm theory of operators on Banach spaces. Properties of the quasi-nilpotent part are investigated and an application is given to totally paranormal and prehermitian operators.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.359-369
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• 2004

The purpose of this paper is to compare the radicals of a left symmetric algebra considered in 〔1〕 when the associated Lie algebra is nilpotent. In this case, we show that all the radicals considered there are equal. We also consider some other radicals and show they are also equal.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.949-959
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• 2012

In general, a class-preserving automorphism of generalized free products of nilpotent groups, amalgamating a cyclic normal subgroup of order 8, need not be an inner automorphism. We prove that every class-preserving automorphism of generalized free products of nitely generated nilpotent groups, amalgamating a cyclic normal subgroup of order less than 8, is inner.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1389-1396
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• 2018

We observe the structure of a kind of unit-IFP ring that is constructed by Antoine, in relation with units and nilpotent elements. This article concerns the same argument in a more general situation, and study the structure of one-sided zero divisors in such rings. We also provide another kind of unit-IFP ring.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.185-201
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• 2023

With the notion of prime submodule defined by F. Raggi et al. we prove that the intersection of all prime submodules of a Goldie module M is a nilpotent submodule provided that M is retractable and M^(Λ)-projective for every index set Λ. This extends the well known fact that in a left Goldie ring the prime radical is nilpotent.