• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.839-851
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• 2020

We define morphic near-ring elements and study their behavior in regular near-rings. We show that the class of left morphic regular near-rings is properly contained between the classes of left strongly regular and unit-regular near-rings.

• 대한수학회보
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• 제50권5호
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• pp.1433-1439
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• 2013

A ring R is called left morphic if $$R/Ra{\simeq_-}l(a)$$ for every $a{\in}R$. Equivalently, for every $a{\in}R$ there exists $b{\in}R$ such that $Ra=l(b)$ and $l(a)=Rb$. A ring R is called left quasi-morphic if there exist $b$ and $c$ in R such that $Ra=l(b)$ and $l(a)=Rc$ for every $a{\in}R$. A result of T.-K. Lee and Y. Zhou says that R is unit regular if and only if $$R[x]/(x^2){\simeq_-}R{\propto}R$$ is morphic. Motivated by this result, we investigate the morphic property of the ring $$S_n=^{def}R[x_1,x_2,{\cdots},x_n]/(\{x_ix_j\})$$, where $i,j{\in}\{1,2,{\cdots},n\}$. The morphic elements of $S_n$ are completely determined when R is strongly regular.

• 한국조경학회지
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• 제29권4호
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• pp.53-66
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• 2001

Modern art has had a great impact on the concepts and the formal attributes of modern landscape design. This study aimed at examining the origins of modern landscape design languages especially in relation to the influence of find art during the modernist age. The formal reductionism of Cubistic paintings finally lead to the formulation of Geometrical Abstractionism which became the basic formal model for ˝Regular Style˝; one of the representative modern landscape style. This Regular Style is mostly based on the formal structure of ´Grids´, which was developed by many landscape designer like Eckbo, Kley and Halprin. On the other hand, the ´Bio-morphic Form´ originally used in Surrealistic Art became the formal model for ˝Organic Style˝; the other representative modern landscape style, developed mostly by the landscape designers like Church, Burle-Mark and Bye. Thus, ´Grids´ and ´Bio-morphic Form´ became the dual icons of modern art and modern landscape design. Although these modern landscape design styles were ground breaking departure from the conventional formal/informal tradition and expanded possibilities in formal experimentations, They also produced several crucial limitations originated from the scientific reductionism and autonomous aesthetics of modern art, like the physical and cultural discontinuation from surrounding environments and the formal alienation from the real life world, which gave rise to the emergence of post-modern thinking of landscape design.