• 대한수학회지
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• 제56권3호
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• pp.723-738
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• 2019

A property of reduced rings is proved in relation with centers, and our argument in this article is spread out based on this. It is also proved that the Wedderburn radical coincides with the set of all nilpotents in symmetric-over-center rings, implying that the Jacobson radical, all nilradicals, and the set of all nilpotents are equal in polynomial rings over symmetric-over-center rings. It is shown that reduced rings are reversible-over-center, and that given reversible-over-center rings, various sorts of reversible-over-center rings can be constructed. The structure of radicals in reversible-over-center and symmetric-over-center rings is also investigated.

• 대한수학회보
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• 제38권1호
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• pp.149-156
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• 2001

In this paper, we initiate the investigation of ring in which all the additive endomorphisms are generated by ring endomorphisms (AGE-rings). This study was motivated by the work on the Sullivan’s Research Problem [11]: Characterize those rings in which every additive endomorphism is a ring endomorphism (AE-rings). The purpose of this paper is to obtain a certain characterization of AGE-rings, and investigate some relations between AGE and LSD-generated rings.

• 대한수학회보
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• 제45권2호
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• pp.285-297
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• 2008

For an endomorphism ${\alpha}$ of a ring R, the endomorphism ${\alpha}$ is called semicommutative if ab=0 implies $aR{\alpha}(b)$=0 for a ${\in}$ R. A ring R is called ${\alpha}$-semicommutative if there exists a semicommutative endomorphism ${\alpha}$ of R. In this paper, various results of semicommutative rings are extended to ${\alpha}$-semicommutative rings. In addition, we introduce the notion of an ${\alpha}$-skew power series Armendariz ring which is an extension of Armendariz property in a ring R by considering the polynomials in the skew power series ring $R[[x;\;{\alpha}]]$. We show that a number of interesting properties of a ring R transfer to its the skew power series ring $R[[x;\;{\alpha}]]$ and vice-versa such as the Baer property and the p.p.-property, when R is ${\alpha}$-skew power series Armendariz. Several known results relating to ${\alpha}$-rigid rings can be obtained as corollaries of our results.

• 대한수학회지
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• 제60권2호
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• pp.407-464
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• 2023

Let R be a commutative ring with identity. The structure theorem says that R is a PIR (resp., UFR, general ZPI-ring, π-ring) if and only if R is a finite direct product of PIDs (resp., UFDs, Dedekind domains, π-domains) and special primary rings. All of these four types of integral domains are Krull domains, so motivated by the structure theorem, we study the prime factorization of ideals in a ring that is a finite direct product of Krull domains and special primary rings. Such a ring will be called a general Krull ring. It is known that Krull domains can be characterized by the star operations v or t as follows: An integral domain R is a Krull domain if and only if every nonzero proper principal ideal of R can be written as a finite v- or t-product of prime ideals. However, this is not true for general Krull rings. In this paper, we introduce a new star operation u on R, so that R is a general Krull ring if and only if every proper principal ideal of R can be written as a finite u-product of prime ideals. We also study several ring-theoretic properties of general Krull rings including Kaplansky-type theorem, Mori-Nagata theorem, Nagata rings, and Noetherian property.

• Tribology and Lubricants
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• 제12권4호
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• pp.7-12
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• 1996

Present study was undertaken to investigate the leakage and friction of self-lubricating piston seal rings. A crank-piston type gas leakage test set-up was constructed. The piston rings were made of PTFE-polyimide composite. The free gap configurations of the seal rings were butt and step types. Eccentric tension rings were used to give the seal rings prepressure between the seal rings and cylinder wall. Two sizes of the tension rings were installed to investigate their effect on the gas leakage and friction of the seal rings. The results showed that step type seal rings are superior than the butt types. High tension spring rings resulted in low leakage and high friction loss. In order to reduce the gas leakage and friction loss of the piston seal rings, there should be compromise between the number of ring stages and prepressure of the tension rings.

• 대한수학회보
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• 제50권5호
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• pp.1711-1723
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• 2013

P. V$\acute{a}$mos called a ring R 2-good if every element is the sum of two units. The ring of all $n{\times}n$ matrices over an elementary divisor ring is 2-good. A (right) self-injective von Neumann regular ring is 2-good provided it has no 2-torsion. Some of the earlier results known to us about 2-good rings (although nobody so called at those times) were due to Ehrlich, Henriksen, Fisher, Snider, Rapharl and Badawi. We continue in this paper the study of 2-good rings by several authors. We give some examples of 2-good rings and their related properties. In particular, it is shown that if R is an exchange ring with Artinian primitive factors and 2 is a unit in R, then R is 2-good. We also investigate various kinds of extensions of 2-good rings, including the polynomial extension, Nagata extension and Dorroh extension.

• Korean Journal of Mathematics
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• 제23권1호
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• pp.37-46
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• 2015

We in this note introduce the concept of semi-IFP rings which is a generalization of IFP rings. We study the basic structure of semi-IFP rings, and construct suitable examples to the situations raised naturally in the process. We also show that the semi-IFP does not go up to polynomial rings.

• 대한수학회보
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• 제44권4호
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• pp.641-649
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• 2007

We in this note introduce a concept, so called ${\pi}-Armendariz$ ring, that is a generalization of both Armendariz rings and 2-primal rings. We first observe the basic properties of ${\pi}-Armendariz$ rings, constructing typical examples. We next extend the class of ${\pi}-Armendariz$ rings, through various ring extensions.

• 대한수학회보
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• 제46권6호
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• pp.1091-1097
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• 2009

In this paper, we investigate the extensions of generalized stable rings. It is shown that a ring R is a generalized stable ring if and only if R has a complete orthogonal set {e$_1$, . . . , e$_n$} of idempotents such that e$_1$Re$_1$, . . . , e$_n$Re$_n$ are generalized stable rings. Also, we prove that a ring R is a generalized stable ring if and only if R[[X]] is a generalized stable ring if and only if T(R,M) is a generalized stable ring.

• 대한수학회지
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• 제47권2호
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• pp.247-261
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• 2010

An associative ring R with identity is called a clean ring if every element of R is the sum of a unit and an idempotent. In this paper, we introduce the concept of f-clean rings. We study various properties of f-clean rings. Let C = $\(\array{A\;V\\W\;B}\)$ be a Morita Context ring. We determine conditions under which the ring C is f-clean. Moreover, we introduce the concept of rings having many full elements. We investigate characterizations of this kind of rings and show that rings having many full elements are closed under matrix rings and Morita Context rings.