• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.915-923
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• 2022

The purpose of the present paper is to obtain commutativity of prime Γ-near-ring N with generalized derivations F and G with associated derivations d and h respectively satisfying one of the following conditions:(i) G([x, y]α = ±f(y)α(xoy)βγg(y), (ii) F(x)βG(y) = G(y)βF(x), for all x, y ∈ N, β ∈ Γ (iii) F(u)βG(v) = G(v)βF(u), for all u ∈ U, v ∈ V, β ∈ Γ,(iv) if 0 ≠ F(a) ∈ Z(N) for some a ∈ V such that F(x)αG(y) = G(y)αF(x) for all x ∈ V and y ∈ U, α ∈ Γ.

• 대한수학회보
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• 제60권5호
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• pp.1281-1293
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• 2023

The purpose of this paper is to study the relationship between the structure of a factor ring R/P and the behavior of some derivations of R. More precisely, we establish a connection between the commutativity of R/P and derivations of R satisfying specific identities involving the prime ideal P. Moreover, we provide an example to show that our results cannot be extended to semi-prime ideals.

• Journal of Applied and Pure Mathematics
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• 제4권1_2호
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• pp.1-7
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• 2022

A mapping T : R → R (not necessarily additive) is called multiplicative left 𝛼-centralizer if T(xy) = T(x)𝛼(y) for all x, y ∈ R. A mapping F : R → R (not necessarily additive) is called multiplicative (generalized)(𝛼, 𝛽)-derivation if there exists a map (neither necessarily additive nor derivation) f : R → R such that F(xy) = F(x)𝛼(y) + 𝛽(x)f(y) for all x, y ∈ R, where 𝛼 and 𝛽 are automorphisms on R. The main purpose of this paper is to study some algebraic identities with multiplicative (generalized) (𝛼, 𝛽)-derivations and multiplicative left 𝛼-centralizer on the left ideal of a prime ring R.

• 호남수학학술지
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• 제32권4호
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• pp.675-687
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• 2010

In this paper the dual notion of tight closure of ideals relative to modules is introduced and some related results are obtained.

• 대한수학회논문집
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• 제10권3호
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• pp.491-498
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• 1995

This paper is concerned with an asymptotic behavior of ideals relative to injective modules ove the commutative Noetherian ring A : under what conditions on A can we show that $$\bar{At^*}(a,E)=At^*(a,E)$?

• 대한수학회보
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• 제46권5호
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• pp.873-884
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• 2009

We characterize QB-ideals of exchange rings by means of quasi-invertible elements and annihilators. Further, we prove that every $2\times2$ matrix over such ideals of a regular ring admits a diagonal reduction by quasi-inverse matrices. Prime exchange QB-rings are studied as well.

• 충청수학회지
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• 제18권1호
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• pp.87-93
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• 2005

For a left R-module M, we identify certain submodules of M that play a role analogous to that of ideals in the ring R. We investigate some properties of M-ideals in the submodules of M and also study Jacobson radicals of a submodule of M.

• 대한수학회지
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• 제34권1호
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• pp.13-21
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• 1997

In recent years M. Hochster and C. Huneke introduced the notions of tight closure of an ideal and of the weak F-regularity of a ring of positive prime characteristic. Here 'F' stands for Frobenius. This notion enabled us to play an important role in a commutative ring theory, and other related topics.

• 대한수학회지
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• 제43권1호
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• pp.65-76
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• 2006

Let $\tau$ be a hereditary torsion theory and let p be a prime ideal of a commutative ring R. We study the existence of (minimal) $\tau-injective$ submodules of the injective hull of R/p.

• Nuclear Engineering and Technology
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• 제50권3호
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• pp.462-469
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• 2018

The background spectrum of a $3^{{\prime}{\prime}}{\times}3^{{\prime}{\prime}}$ NaI(Tl) well-type scintillation SILENA detector was measured without shielding, in 6 cm thick lead shielding, and with 2 mm thick electrolytic copper covering the detector inside the lead shielding. The relative remaining background of the lead shield lined with copper was found to be ideal for low-level environmental radioactive spectroscopy. The background total count rate in the (20-2160 KeV) was reduced 28.7 times by the lead and 29 times by the Cu + Pb shielding. The effective reduction of background (1.04) by the copper mainly appeared in the energy range from X-ray up to 500 KeV, while for the total energy range the ratio is 1.01 relative to the lead only. In addition, a strong relation between the full-energy peak absolute efficiency and the detector well height was found using gamma-ray isotropic radiation point sources placed inside the detector well. The full-energy peak efficiency at a midpoint of the well (at 2.5 cm) is three times greater than that on the detector surface. The energy calibrations and the resolution of any single energy line are independent of the locations of the gamma source inside or outside of the well.