• Korean Journal of Mathematics
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• v.22 no.2
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• pp.279-288
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• 2014

The studies of reversible and 2-primal rings have done important roles in noncommutative ring theory. We in this note introduce the concept of quasi-reversible-over-prime-radical (simply, QRPR) as a generalization of the 2-primal ring property. A ring is called QRPR if ab = 0 for $a,b{\in}R$ implies that ab is contained in the prime radical. In this note we study the structure of QRPR rings and examine the QRPR property of several kinds of ring extensions which have roles in noncommutative ring theory.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.65-73
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• 2020

This article concerns a property of local rings and domains. A ring R is called weakly local if for every a ∈ R, a is regular or 1-a is regular, where a regular element means a non-zero-divisor. We study the structure of weakly local rings in relation to several kinds of factor rings and ring extensions that play roles in ring theory. We prove that the characteristic of a weakly local ring is either zero or a power of a prime number. It is also shown that the weakly local property can go up to polynomial (power series) rings and a kind of Abelian matrix rings.

• Kyungpook Mathematical Journal
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• v.51 no.1
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• pp.1-10
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• 2011

Let (R, T) be a normal pair of commutative rings (i.e., R ${\subseteq}$ T is a unita extension of commutative rings, not necessarily integral domains, such that S is integrally closed in T for each ring S such that R ${\subseteq}$ S ${\subseteq}$ T) such that the total quotient ring of R is a von Neumann regular ring. Let P be one of the following ring-theoretic properties: going-down ring, extensionally going-down (EGD) ring, locally divided ring. Then R has P if and only if T has P. An example shows that the "if" part of the assertion fails if P is taken to be the "divided domain" property.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.367-377
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• 2024

Let G = (V, E) be a graph with p-vertices and q-edges and let R^◦ be a finite zero ring of order n. An injective function f : V (G) → {r₁, r₂, _…, r_k}, where r_i ∈ R^◦ is called vertex pair sum k-zero ring labeling, if it is possible to label the vertices x ∈ V with distinct labels from R^◦ such that each edge e = uv is labeled with f(e = uv) = [f(u) + f(v)] (mod n) and the edge labels are distinct. A graph admits such labeling is called vertex pair sum k-zero ring graph. The minimum value of positive integer k for a graph G which admits a vertex pair sum k-zero ring labeling is called the vertex pair sum k-zero ring index denoted by 𝜓_pz(G). In this paper, we defined the vertex pair sum k-zero ring labeling and applied to some graphs.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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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.

• Korean Journal of Mathematics
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• v.21 no.1
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• pp.29-34
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• 2013

Power-Armendariz is a unifying concept of Armendariz and commutative. Let R be a ring and I be a proper ideal of R such that R/I is a power-Armendariz ring. Han et al. proved that if I is a reduced ring without identity then R is power-Armendariz. We find another direct proof of this result to see the concrete forms of various kinds of subsets appearing in the process.

• The Korean Journal of Cytopathology
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• v.13 no.2
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• pp.88-92
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• 2002

Scattered single cells or variable sized clusters of signet ring cells in the aspirated smears of breast lesions are almost exclusively associated with carcinoma. The signet ring cells are defined as those containing a prominent intracytoplasmic vacuole or amorphous cytoplasm diffusely dispersed with mucin. The primary signet ring cell carcinoma of the breast behaves more aggressively than carcinoma without signet ring cells. Therefore, it is very important to make a correct diagnosis of signet ring cell carcinoma. Fine needle aspiration cytology is useful for diagnosis of breast lesions Including signet ring cell carcinoma. We report two cases, which showed mostly signet ring cells in the aspirated smears of the breast. One case consisted of numerous individual signet ring cells and variable sized cell clusters in rather mucoid background. The tumor cells had abundant amorphous cytoplasm filled with dispersed mucin or occasionally mucin vacuoles(PAS +) and eccentric nuclei. The resected mass revealed mucinous carcinoma. The other showed the cytologic findings of low cellularity, and small loosely cohesive signet ring cell clusters with mild nuclear pleomorphism. It was confirmed as lobular signet ring cell carcinoma in the resected tumor.

• The Korean Journal of Cytopathology
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• v.14 no.2
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• pp.66-70
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• 2003

Signet ring cell carcinoma is a rare type of mucinous adenocarcinoma of the uterine cervix. To the best of our knowledge, there is no report on cytologlc findings of primary signet ring cell carcinoma of the uterine cervix in the literature. Recently, we experienced two cases of signet ring cell carcinoma of the uterine cervix. The finding of characteristic signet ring cells on cervicovaginal smear led to the diagnosis of signet ring cell carcinoma. However, primary signet ring cell carcinoma could not be cytologically distinguished from more common metastatic tumor. Therefore, diagnosis rests upon the recognition of signet ring cells and the absence of signet ring cell carcinoma elsewhere.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.51-69
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• 2017

We, in this paper, study the commutativity of skew polynomials at zero as a generalization of an ${\alpha}-rigid$ ring, introducing the concept of strongly skew reversibility. A ring R is be said to be strongly ${\alpha}-skew$ reversible if the skew polynomial ring $R[x;{\alpha}]$ is reversible. We examine some characterizations and extensions of strongly ${\alpha}-skew$ reversible rings in relation with several ring theoretic properties which have roles in ring theory.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.2
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• pp.191-196
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• 2004