• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.04a
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• pp.179-182
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• 2007

In this paper, we introduce the concepts of fuzzy (r, s)-semi-preopen sets and fuzzy (r, s)-semi-precontinuous maps on intuitionistic fuzzy topological spaces in Sostak's sense. The relations among fuzzy (r, s)-semicontinuous, fuzzy (r, s)-precontinuous, and fuzzy (r, s)-semi-precontinuous maps are discussed. The concepts of fuzzy (r, s)-semi-preinterior, fuzzy (r, s)-semi-preclosure, fuzzy (r, s)-semi-preneighborhood, and fuzzy (r, s)-quasi-semi-preneighborhood are given. Using these concepts, the characterization for the fuzzy (r, s)-semi-precontinuous map is obtained. Also, we introduce the notions of fuzzy (r, s)-semi-preopen and fuzzy (r, s)-semi-preclosed maps on intuitionistic fuzzy topological spaces in Sostak's sense, and then we investigate some of their characteristic properties.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.49-57
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• 2007

Using the idea of degree of openness and degree of nonopenness, Coker and Demirci [5] defined intuitionistic fuzzy topological spaces in Sostak's sense as a generalization of smooth topological spaces and intuitionistic fuzzy topological spaces. M. N. Mukherjee and S. P. Sinha [10] introduced the concept of fuzzy irresolute maps on Chang's fuzzy topological spaces. In this paper, we introduce the concepts of fuzzy (r,s)-irresolute, fuzzy (r,s)-presemiopen, fuzzy almost (r,s)-open, and fuzzy weakly (r,s)-continuous maps on intuitionistic fuzzy topological spaces in Sostak's sense. Using the notions of fuzzy (r,s)-neighborhoods and fuzzy (r,s)-semineighborhoods of a given intuitionistic fuzzy points, characterizations of fuzzy (r,s)-irresolute maps are displayed. The relations among fuzzy (r,s)-irresolute maps, fuzzy (r,s)-continuous maps, fuzzy almost (r,s)-continuous maps, and fuzzy weakly (r,s)-cotinuous maps are discussed.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.4
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• pp.550-556
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• 2007

In this paper, we introduce the concepts of fuzzy (r, s)-semi-preopen sets and fuzzy (r, s)-semi-precontinuous mappings on intuitionistic fuzzy topological spaces in ${\check{S}}ostak's$ sense. The relations among fuzzy (r, s)-semicontinuous, fuzzy (r, s)-precontinuous, and fuzzy (r, s)-semi-precontinuous mappings we discussed. The concepts of fuzzy (r, s)-semi-preinterior, fuzzy (r, s)-semi-preclosure, fuzzy (r, s)-semi-preneighborhood, and fuzzy (r, s)-quasi-semi-preneighborhood are given. Using these concepts, the characterization for the fuzzy (r, s)-semi-precontinuous mapping is obtained. Also, we introduce the notions of fuzzy (r, s)-semi-preopen and fuzzy (r, s)-semi-preclosed mappings on intuitionistic fuzzy topological spaces in ${\check{S}}ostak's$ sense, and then we investigate some of their characteristic properties.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.191-194
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• 2007

In this paper, we introduce the concepts of fuzzy (r,s)-pre-semiopen sets and fuzzy (r,s)-pre-semicontinuous mappings on intuitionistic fuzzy topological spaces in ${\v{S}}ostak's$ sense. The concepts of fuzzy (r,s)-pre-semiinterior, fuzzy (r,s)-pre-semiclosure, fuzzy (r,s)-pre-semineighborhood, and fuzzy (r,s)-quasi-pre-semineighborhood are given, and several properties of these concepts are discussed. Using these concepts, the characterizations for the fuzzy (r,s)-pre-semicontinuous mappings are obtained. Also, we introduce the notions of fuzzy (r,s)-presemiopen and fuzzy (r,s)-pre-semiclosed mappings on intuitionistic fuzzy topologica spaces in ${\v{S}}ostak's$ sense, and then we investigate some of their characteristic properties.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.643-657
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• 2022

Let R be a ring and S a multiplicative subset of R. An R-module T is called u-S-torsion (u-always abbreviates uniformly) provided that sT = 0 for some s ∈ S. The notion of u-S-exact sequences is also introduced from the viewpoint of uniformity. An R-module F is called u-S-flat provided that the induced sequence 0 → A ⊗_R F → B ⊗_R F → C ⊗_R F → 0 is u-S-exact for any u-S-exact sequence 0 → A → B → C → 0. A ring R is called u-S-von Neumann regular provided there exists an element s ∈ S satisfying that for any a ∈ R there exists r ∈ R such that sα = rα². We obtain that a ring R is a u-S-von Neumann regular ring if and only if any R-module is u-S-flat. Several properties of u-S-flat modules and u-S-von Neumann regular rings are obtained.

• Korean Journal of Breeding Science
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• v.42 no.1
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• pp.50-55
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• 2010

The R-r:standard (R-r:std) allele of maize R gene complex consists of S subcomplex and P component; the S subcomplex regulates anthocyanin pigmentation of seed aleurone layer, and the P component confers pigmentation of the other plant parts. The S subcomplex contains two functional genes, S1 and S2 components. In the presence of Pl gene some alleles of R gene induce anthocyanin pigmentation of pericarp. In the present study, the effects of different R alleles on the anthocyanin pigmentation of pericarp in the presence of Pl gene were analyzed in order to identify the R gene component responsible for pericarp pigmentation. The results show that R-ch and r-ch alleles condition similar degrees of pericarp pigmentation, and that R-r:Ecuador (R-r:Ec) conditions stronger pigmentation. The r-ch allele, which is inferred that its S subcomplex has lost function but the P component is normal, induces pericarp pigmentation in the presence of Pl gene. On the contrary, the R-g:g1111 allele, derived from R-r:Ec and inferred that its S subcomplex functions normal but the P component has lost its function, did not induce pericarp pigmentation in the presence of Pl gene. Moreover, PCR analysis of genomic DNA's of R-ch and r-ch indicate that R-ch maintains both P and S1 components, whereas r-ch lacks for the S1 component. Taken together, The results suggest that the P components of R alleles inducing pericarp pigmentation in the presence of Pl gene are responsible for pericarp pigmentation.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.139-143
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• 2015

In this paper, we prove that (r, s)-semi-irresolute image of the (r, s)-semi-${\theta}$-connected set is also (r, s)-semi-${\theta}$-connected. Moreover, we prove that an (r, s)-semi-irresolute mapping preserves (r; s)-$S^*$-closedness.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.617-622
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• 2021

Let R be a commutative ring with identity, R[X] the polynomial ring over R and S a multiplicative subset of R. Let U = {f ∈ R[X] | f is monic} and let N = {f ∈ R[X] | c(f) = R}. In this paper, we show that if S is an anti-Archimedean subset of R, then R is an S-Noetherian ring if and only if R[X]_U is an S-Noetherian ring, if and only if R[X]_N is an S-Noetherian ring. We also prove that if R is an integral domain and R[X]_U is an S-principal ideal domain, then R is an S-principal ideal domain.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1351-1365
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• 2020

Let S and T be w-linked extension domains of a domain R with S ⊆ T. In this paper, we define what satisfying the w_R-GD property for S ⊆ T means and what being w_R- or w-GD domains for T means. Then some sufficient conditions are given for the w_R-GD property and w_R-GD domains. For example, if T is w_R-integral over S and S is integrally closed, then the w_R-GD property holds. It is also given that S is a w_R-GD domain if and only if S ⊆ T satisfies the w_R-GD property for each w_R-linked valuation overring T of S, if and only if S ⊆ (S[u])_w satisfies the w_R-GD property for each element u in the quotient field of S, if and only if S_𝔪 is a GD domain for each maximal w_R-ideal 𝔪 of S. Then we focus on discussing the relationship among GD domains, w-GD domains, w_R-GD domains, Prüfer domains, PνMDs and Pw_RMDs, and also provide some relevant counterexamples. As an application, we give a new characterization of Pw_RMDs. We show that S is a Pw_RMD if and only if S is a w_R-GD domain and every w_R-linked overring of S that satisfies the w_R-GD property is w_R-flat over S. Furthermore, examples are provided to show these two conditions are necessary for Pw_RMDs.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.661-667
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• 2011

In this paper, we introduce the notions of fuzzy strongly (r, s)-preopen and preclosed mappings on intuitionistic fuzzy topological spaces in $\check{S}$ostak's sense. The relationships among fuzzy (r, s)-open, fuzzy strongly (r, s)-semiopen, fuzzy (r, s)-preopen, and fuzzy strongly (r, s)-preopen mappings are discussed. The characterizations for the fuzzy strongly (r, s)-preopen and preclosed mappings are obtained.