• 한국수학교육학회지시리즈E:수학교육논문집
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• 제10권
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• pp.283-292
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• 2000

We shall introduce new concepts of near-rings, that is, strong reducibility and left semi ${\pi}$-regular near-rings. We will study every strong reducibility of near-ring implies reducibility of near-ring but this converse is not true, and also some characterizations of strong reducibility of near-rings. We shall investigate some relations between strongly reduced near-rings and left strongly regular near-rings, and apply strong reducibility of near-rings to the study of left semi ${\pi}$-regular near-rings, s-weekly regular near-rings and some other regularity of near-rings.

• 충청수학회지
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• 제22권3호
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• pp.293-297
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• 2009

We will introduce some properties of strongly reduced near-rings and the notion of left $\pi$-regular near-ring. Also, we will study for right $\pi$-regular, strongly left $\pi$-regular, strongly right $\pi$-regular and strongly $\pi$- regular. Next, we may characterize the strongly $\pi$-regular near-rings with related strong reducibility.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권4호
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• pp.199-206
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• 2003

Let N be a right near-ring. N is said to be strongly reduced if, for $a\inN$, $a^2 \in N_{c}$ implies $a\;\in\;N_{c}$, or equivalently, for $a\inN$ and any positive integer n, $a^{n} \in N_{c}$ implies $a\;\in\;N_{c}$, where $N_{c}$ denotes the constant part of N. We will show that strong reducedness is equivalent to condition (ⅱ) of Reddy and Murty's property $(^{\ast})$ (cf. [Reddy & Murty: On strongly regular near-rings. Proc. Edinburgh Math. Soc. (2) 27 (1984), no. 1, 61-64]), and that condition (ⅰ) of Reddy and Murty's property $(^{\ast})$ follows from strong reducedness. Also, we will investigate some characterizations of strongly reduced near-rings and their properties. Using strong reducedness, we characterize left strongly regular near-rings and ($P_{0}$)-near-rings.

• 호남수학학술지
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• 제42권1호
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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.