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- 저자 : Shokuhifar, (검색결과 5 건)
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ON SOME TYPE ELEMENTS OF ZERO-SYMMETRIC NEAR-RING OF POLYNOMIALS
Hashemi, Ebrahim,Shokuhifar, Fatemeh Korean Mathematical Society 2019 대한수학회지 Vol.56 No.1
Let R be a commutative ring with unity. In this paper, we characterize the unit elements, the regular elements, the ${\pi}$-regular elements and the clean elements of zero-symmetric near-ring of polynomials $R_0[x]$, when $nil(R)^2=0$. Moreover, it is shown that the set of ${\pi}$-regular elements of $R_0[x]$ forms a semigroup. These results are somewhat surprising since, in contrast to the polynomial ring case, the near-ring of polynomials has substitution for its "multiplication" operation.
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On some type elements of zero-symmetric near-ring of polynomials
Ebrahim Hashemi,Fatemeh Shokuhifar 대한수학회 2019 대한수학회지 Vol.56 No.1
Let $R$ be a commutative ring with unity. In this paper, we characterize the unit elements, the regular elements, the $\pi$-regular elements and the clean elements of zero-symmetric near-ring of polynomials $R_{0}[x]$, when $ \mathrm{nil}(R)^{2}=0 $. Moreover, it is shown that the set of $\pi$-regular elements of $R_{0}[x]$ forms a semigroup. These results are somewhat surprising since, in contrast to the polynomial ring case, the near-ring of polynomials has substitution for its ``multiplication'' operation.
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ON THE STRUCTURE OF ZERO-DIVISOR ELEMENTS IN A NEAR-RING OF SKEW FORMAL POWER SERIES
Alhevaz, Abdollah,Hashemi, Ebrahim,Shokuhifar, Fatemeh Korean Mathematical Society 2021 대한수학회논문집 Vol.36 No.2
The main purpose of this paper is to study the zero-divisor properties of the zero-symmetric near-ring of skew formal power series R<sub>0</sub>[[x; α]], where R is a symmetric, α-compatible and right Noetherian ring. It is shown that if R is reduced, then the set of all zero-divisor elements of R<sub>0</sub>[[x; α]] forms an ideal of R<sub>0</sub>[[x; α]] if and only if Z(R) is an ideal of R. Also, if R is a non-reduced ring and annR(a - b) ∩ Nil(R) ≠ 0 for each a, b ∈ Z(R), then Z(R<sub>0</sub>[[x; α]]) is an ideal of R<sub>0</sub>[[x; α]]. Moreover, if R is a non-reduced right Noetherian ring and Z(R<sub>0</sub>[[x; α]]) forms an ideal, then ann<sub>R</sub>(a - b) ∩ Nil(R) ≠ 0 for each a, b ∈ Z(R). Also, it is proved that the only possible diameters of the zero-divisor graph of R<sub>0</sub>[[x; α]] is 2 and 3.
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An Alternative Perspective of Near-rings of Polynomials and Power series
Ebrahim Hashemi,Fatemeh Shokuhifar,Abdollah Alhevaz 경북대학교 자연과학대학 수학과 2022 Kyungpook mathematical journal Vol.62 No.3
Unlike for polynomial rings, the notion of multiplication for the near-ring of polynomials is the substitution operation. This leads to somewhat surprising results. Let S be an abelian left near-ring with identity. The relation ∼ on S defined by letting a ∼ b if and only if annS(a) = annS(b), is an equivalence relation. The compressed zero-divisor graph ΓE(S) of S is the undirected graph whose vertices are the equivalence classes in duced by ∼ on S other than [0]S and [1]S, in which two distinct vertices [a]S and [b]S are adjacent if and only if ab = 0 or ba = 0. In this paper, we are interested in studying the compressed zero-divisor graphs of the zero-symmetric near-ring of polynomials R0[x] and the near-ring of the power series R0[[x]] over a commutative ring R. Also, we give a complete characterization of the diameter of these two graphs. It is natural to try to find the relationship between diam.
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Nasim Shams,Mahshid Razavi,Mansour Zabihzadeh,Mohammadreza Shokuhifar,Vahid Rakhshan 대한악안면성형재건외과학회 2022 Maxillofacial Plastic Reconstructive Surgery Vol.44 No.-
Background: Nasal septum deviation (NSD) can cause serious anatomical and clinical complications. It can changethe breathing pattern and thus alter the anatomy of the airway structures. Despite its importance, the associationbetween NSD with the nasopharynx volume (NPV) has not been assessed before. Therefore, we aimed to investigateit for the first time. Methods: Archival CBCTs of 202 patients older than 17 years and without any history of trauma or pathology of thenasopharynx and without any orthodontic/orthognathic treatments were evaluated (129 women, 73 men, meanage: 36.24 ± 14.61 years). All included CBCTs must have been taken with a 12 × 8 field of view and fully covered thenasopharynx areas. The extent of NSD (°) and NPV (mm3) were measured. NSDs were categorized as mild (NSD ? 9°),moderate (9 ≤ NSD ≤ 15°), and severe (NSD ? 15°). Associations between sex, age, NSD, and nasopharynx volumewere assessed using independent-samples t test, chi-square, one-way ANOVA, Tamhane post hoc test, Pearson andpoint-biserial correlation coefficients, and multiple linear regressions (α = 0.05). Results: Mean NSDs were 11.27 ± 4.69° (range 1?19.5), 11.58 ± 4.63°, and 10.70 ± 4.76° in the sample, females, andmales, respectively (P > 0.05). Of females, 27.9%, 40.3%, and 31.8% had mild, moderate, and severe NSDs. These were35.6%, 39.7%, and 24.7% in males (P > 0.05). Mean NPVs were 4.88 ± 1.49, 4.80 ± 1.43, and 5.04 ± 1.60 mm3in thesample, females, and males, respectively (P > 0.05). Mean NPVs were 6.41 ± 1.21, 4.87 ± 0.73, and 3.30 ± 0.65 mm3inmild, moderate, and severe NSD groups (all P values = 0.000). Mean ages were 27.06 ± 6.49, 29.80 ± 9.64, and 54.73± 8.45 years in mild, moderate, and severe NSD groups (severe group being older than the other two groups, P =0.000). NSD was strongly, negatively correlated with NPV (R = ? 0.793, P = 0.000). Sex was not correlated with NPV orNSD (P ≥ 0.189). Age was negatively and positively correlated with NPV and NSD, respectively (P = 0.000). ModelingNSD (β = ?0.776, P = 0.000) as a predictor for NPV rendered age effect insignificant (P > 0.05). Conclusions: It was found, for the first time, that the more deviated the nasal septum, the smaller the nasopharynxvolume. Aging might increase NSD and through it, reduce the nasopharynx volume. Sex might not affect NSD or NPV.
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