• 대한수학회보
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• 제48권1호
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• pp.115-127
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• 2011

We study the structure of the set of nilpotent elements in various kinds of ring and introduce the concept of NR ring as a generalization of Armendariz rings and NI rings. We determine the precise relationships between NR rings and related ring-theoretic conditions. The Kothe's conjecture is true for the class of NR rings. We examined whether several kinds of extensions preserve the NR condition. The classical right quotient ring of an NR ring is also studied under some conditions on the subset of nilpotent elements.

• 호남수학학술지
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• 제27권3호
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• pp.399-404
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• 2005

Let M be a finite commutative nilpotent algebra over a perfect field k of prime characteristic p and let $M^p$ be the sub-algebra of M generated by $x^p$, $x{\in}M$. Eggert[3] conjectures that $dim_kM{\geq}pdim_kM^p$. In this paper, we show that the conjecture holds for $M=R^+/I$, where $R=k[X_1,\;X_2,\;{\cdots},\;X_t]$ is a polynomial ring with indeterminates $X_1,\;X_2,\;{\cdots},\;X_t$ over k and $R^+$ is the maximal ideal of R generated by $X_1,\;X_2,{\cdots},\;X_t$ and I is a monomial ideal of R containing $X_1^{n_1+1},\;X_2^{n_2+1},\;{\cdots},\;X_t^{n_t+1}$ ($n_i{\geq}0$ for all i).

• 논리연구
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• 제14권1호
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• pp.55-76
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• 2011

이 논문은 uninorm의 한 체계인 WUML(Weak Uninorm Mingle Logic)을 다룬다. 먼저 WUML을 도입하고, 그 체계에 상응하는 대수적 구조를 정의한다. 그런 다음 그 체계의 대수적 완전성을 증명한다. 끝으로 WUML과 IUML의 표준적 완전성을 증명한다.

• 충청수학회지
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• 제6권1호
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• pp.89-94
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• 1993

The main goal of the present paper is to investigate conditions for the separating ideal of a Banach algebra to be nilpotent.

• East Asian mathematical journal
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• 제35권3호
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• pp.277-283
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• 2019

In this article we show that direct limits do not preserve the property that the Wedderburn radical contains all nilpotents, comparing the fact that the NI property is preserved by direct limits.

• 호남수학학술지
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• 제38권2호
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• pp.317-323
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• 2016

In this paper, we show that for every $N{\in}\mathbb{N}$, isometric N-Jordan operators on Hilbert spaces are power regular. Moreover, the only normaloid or 2-isometric, N-Jordan operators are isometries.

• East Asian mathematical journal
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• 제36권3호
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• pp.331-335
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• 2020

We consider HNN extensions 〈B, t : t^―1Ht = K〉, where H, K are in the center of B. We show that conjugating automorphisms of those HNN extensions are inner if B satisfies certain conditions.

• 대한수학회논문집
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• 제11권2호
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• pp.303-310
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• 1996

We define a group property of finite base which is closely related to finite Pr$\ddot{u}$fer rank, and then study the class of groups having such a property.

• 대한수학회논문집
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• 제31권3호
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• pp.461-466
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• 2016

In general, polygonal products of free groups are not residually finite. Using the residual finiteness of polygonal products of nilpotent groups, we show that certain polygonal products of free groups are residually finite.

• 대한수학회지
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• 제49권2호
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• pp.343-356
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• 2012

In this paper, we consider the canonical cusps in complex hyperbolic surfaces. We will classify canonical cusps in complex hyper-bolic surfaces and find correspondence between them and 3-dimensiona nilpotent groups. This paper is a sequel of our paper [6].