• Journal of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.35-57
• /
• 2017

In this paper, we study the natural star-operation defined by the set of associated primes of principal ideals of an integral domain, which is called the g-operation. We are mainly concerned with the ideal-theoretic properties of this star-operation. In particular, we investigate DG-domains (i.e., integral domains in which each ideal is a g-ideal), which form a proper subclass of the DW-domains. In order to provide some original examples, we examine the transfer of the DG-property to pullbacks. As an application of the g-operation, it is shown that w-divisorial Mori domains can be seen as a Gorenstein analogue of Krull domains.

• Communications of the Korean Mathematical Society
• /
• v.39 no.2
• /
• pp.363-372
• /
• 2024

In this paper, we introduce a weak version of coherent that we call regular coherent property. A ring is called regular coherent, if every finitely generated regular ideal is finitely presented. We investigate the stability of this property under localization and homomorphic image, and its transfer to various contexts of constructions such as trivial ring extensions, pullbacks and amalgamated. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.

• Journal of the Korean Mathematical Society
• /
• v.53 no.3
• /
• pp.623-643
• /
• 2016

In this paper, we study piecewise Noetherian (resp., piecewise w-Noetherian) properties in several settings including flat (resp., t-flat) overrings, Nagata rings, integral domains of finite character (resp., w-finite character), pullbacks of a certain type, polynomial rings, and D + XK[X] constructions.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.1093-1101
• /
• 2018

Let (RDTF, M) be a Milnor square. In this paper, it is proved that R is a ${\mathcal{C}}$-hereditary domain if and only if both D and T are ${\mathcal{C}}$-hereditary domains; R is an almost perfect domain if and only if D is a field and T is an almost perfect domain; R is a Matlis domain if and only if T is a Matlis domain. Furthermore, to give a negative answer to Lee, s question, we construct a counter example which is a C-hereditary domain R with $w.gl.dim(R)={\infty}$.

• Korean Circulation Journal
• /
• v.54 no.1
• /
• pp.30-39
• /
• 2024

Background and Objectives: Intravascular ultrasound (IVUS) evaluation of coronary artery morphology is based on the lumen and vessel segmentation. This study aimed to develop an automatic segmentation algorithm and validate the performances for measuring quantitative IVUS parameters. Methods: A total of 1,063 patients were randomly assigned, with a ratio of 4:1 to the training and test sets. The independent data set of 111 IVUS pullbacks was obtained to assess the vessel-level performance. The lumen and external elastic membrane (EEM) boundaries were labeled manually in every IVUS frame with a 0.2-mm interval. The Efficient-UNet was utilized for the automatic segmentation of IVUS images. Results: At the frame-level, Efficient-UNet showed a high dice similarity coefficient (DSC, 0.93±0.05) and Jaccard index (JI, 0.87±0.08) for lumen segmentation, and demonstrated a high DSC (0.97±0.03) and JI (0.94±0.04) for EEM segmentation. At the vessel-level, there were close correlations between model-derived vs. experts-measured IVUS parameters; minimal lumen image area (r=0.92), EEM area (r=0.88), lumen volume (r=0.99) and plaque volume (r=0.95). The agreement between model-derived vs. expert-measured minimal lumen area was similarly excellent compared to the experts' agreement. The model-based lumen and EEM segmentation for a 20-mm lesion segment required 13.2 seconds, whereas manual segmentation with a 0.2-mm interval by an expert took 187.5 minutes on average. Conclusions: The deep learning models can accurately and quickly delineate vascular geometry. The artificial intelligence-based methodology may support clinicians' decision-making by real-time application in the catheterization laboratory.