• Honam Mathematical Journal
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• v.34 no.2
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• pp.135-144
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• 2012

falling subalgebra/ideal of a BCK/BCI-algebra is introduced. Relations between falling subalgebras and falling ideals are given. Relations between fuzzy subalgebras/ideals and falling sub-algebras/ideals are provided. A characterization of a falling ideal is established.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.275-278
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• 1994

In 1966, Iseki [4] introduced the notion of BCI-algebras which is a generalization of BCK-algebras. The ideal theory plays an important role in studying BCK/BCI-algebras. In this paper we study decompositions of ideals in BCI-algebras, and give a characterization of closed ideals. Also we define ignorable ideals in BCI-algebras, and investigates its properties.(omitted)

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.51-62
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• 2015

Pseudo-ŁBCK-algebras are commutative pseudo-BCK-algebras with relative cancellation property. In the paper, we introduce fuzzy prime ideals in pseudo-ŁBCK-algebras and investigate some of their properties. We also give various characterizations of prime ideals and fuzzy prime ideals. Moreover, we present conditions for a pseudo-ŁBCKalgebra to be a pseudo-ŁBCK-chain.

• The Pure and Applied Mathematics
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• v.14 no.3
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• pp.223-230
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• 2007

We give an answer to the following question: Question. Let S be a subset of [0,1] containing a maximal element m > 0 and let C :=$\{I_{t}\;{\mid}\;t{\in}S\}$ be a decreasing chain of ideals of a BCK/BCI-algebra X. Then does there exists a fuzzy ideal ${\mu}(X)=S\;and\;C_{\mu}=C?$.

• Honam Mathematical Journal
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• v.40 no.3
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• pp.539-548
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• 2018

The notions of Smarandache (positive implicative, commutative, implicative) d-algebras, Smarandache subalgebras of Smarandache d-algebras and Smarandache BCK-ideals(d-ideals) of a Smarandache d-algebras are introduced. Examples are given, and several related properties are investigated.

• The Pure and Applied Mathematics
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• v.18 no.1
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• pp.41-50
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• 2011

Based on the theory of falling shadows and fuzzy sets, the notion of a falling fuzzy commutative ideal of a BCK-algebra is introduced. Relations between falling fuzzy commutative ideals and falling fuzzy ideals are investigated.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.339-348
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• 2015

Using the notion of soft sets, the concepts of the soft transfer, support and soft algebraic extension of an int-soft subalgebra and ideal in BCK/BCI-algebras are introduced, and related properties are investigated. Conditions for a soft set to be an int-soft subalgebra and ideal are provided. Regarding the notion of support, conditions for the soft transfer of a soft set to be an int-soft subalgebra and ideal are considered.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.395-404
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• 2020

Based on a sub-BCK-algebra K of a BCI-algebra X, the notions of fuzzy (K, ε)-subalgebras, fuzzy (K, ε)-ideals and fuzzy commutative (K, ε)-ideals are introduced, and their relations/properties are investigated. Conditions for a fuzzy subalgebra/ideal to be a fuzzy (K, ε)-subalgebra/ideal are provided.

• 한국균학회소식:학술대회논문집
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• 2018.05a
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• pp.11-11
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• 2018

Cryphonectria parasitica, chestnut blight fungus, has a characteristic of decreasing pathogenicity when infected with Cryphonectria hypovirus 1. C. parasitica is known to be one of the most representative model systems used to observe the interaction between viruses, plants and fungi. The mitogen-activated protein kinase (MAPK) pathway, which is well conserved in various organisms ranging from yeast to humans, functions in relaying phosphorylation-dependent signals within MAPK cascades to diverse cellular functions involved in the regulation of pheromone, cell wall integrity, and osmotolerance in filamentous fungi. Several genes in the MAPK pathway were revealed to be regulated by hypovirus, or to be involved in pathogenicity in C. parasitica. Among these pathways, the CWI pathway has aroused interest because CpBck1, an ortholog of yeast Bck1 (a CWI MAPKKK), was previously reported to be involved in cell wall integrity and sectorization. Interestingly, sporadic sectorization was observed in the CpBck1 mutant and sectored phenotypes were stably inherited in the progeny that were successively transferred from sectored mycelia. In this study, we analyzed the biological function of CpSlt2, downstream gene of CpBck1, to confirm whether the sectorization phenomenon occurred in the specific single gene or cell wall integrity (CWI) pathway. As results, the CpSlt2-null mutant exhibited marked changes in colonial growth, near absence of conidiation and aerial hyphae, abnormal pigmentation, CWI-related phenotypic defects, and dramatically impaired virulence. As cultivation of the mutant strains progressed, the majority of the colonies showed sporadic sectorization and mycelia from the sectored area stably maintained the sectored phenotype. These results suggest that the unique sectorization is CWI pathway-specific, though the components in the same CWI pathway have common and specific functions.

• Molecules and Cells
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• v.42 no.4
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• pp.363-375
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• 2019

Fungal sectorization is a complex trait that is still not fully understood. The unique phenotypic changes in sporadic sectorization in mutants of CpBck1, a mitogen-activated protein kinase kinase kinase (MAPKKK) gene, and CpSlt2, a mitogen-activated protein kinase (MAPK) gene, in the cell wall integrity pathway of the chestnut blight fungus Cryphonectria parasitica have been previously studied. Although several environmental and physiological factors cause this sectoring phenotype, genetic variants can also impact this complex morphogenesis. Therefore, RNA sequencing analysis was employed to identify candidate genes associated with sectorization traits and understand the genetic mechanism of this phenotype. Transcriptomic analysis of CpBck1 and CpSlt2 mutants and their sectored progeny strains revealed a number of differentially expressed genes (DEGs) related to various cellular processes. Approximately 70% of DEGs were common between the wild-type and each of CpBck1 and CpSlt2 mutants, indicating that CpBck1 and CpSlt2 are components of the same MAPK pathway, but each component governs specific sets of genes. Functional description of the DEGs between the parental mutants and their sectored progenies revealed several key pathways, including the biosynthesis of secondary metabolites, translation, amino acid metabolism, and carbohydrate metabolism; among these, pathways for secondary metabolism and translation appeared to be the most common pathway. The results of this comparative study provide a better understanding of the genetic regulation of sector formation and suggest that complex several regulatory pathways result in interplays between secondary metabolites and morphogenesis.