• Honam Mathematical Journal
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• v.28 no.3
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• pp.327-332
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• 2006

Prime elements and ${\bigwedge}$-irreducible elements are introduced, and related properties are investigated.

• The Transactions of the Korea Information Processing Society
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• v.7 no.9
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• pp.2913-2919
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• 2000

It is essential to get large prime numbers in the design of asymmetric encryption algorithm. However, the pseudoprime numbers with high possibility to be primes have been generally used in the asymmetric encryption algorithms, because it is very difficult to find large deterministic prime numbers. In this paper, we propose a new method of deterministic prime number generation. The prime numbers generated by the proposed method have a 100% precise prime characteristic. They are also guaranteed reliability, security strength, and an ability of primitive element generation.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.1-9
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• 2023

An le-module M over a commutative ring R is a complete lattice ordered additive monoid (M, ⩽, +) having the greatest element e together with a module like action of R. This article characterizes the le-modules _RM such that the pseudo-prime spectrum X_M endowed with the Zariski topology is a Noetherian topological space. If the ring R is Noetherian and the pseudo-prime radical of every submodule elements of _RM coincides with its Zariski radical, then X_M is a Noetherian topological space. Also we prove that if R is Noetherian and for every submodule element n of M there is an ideal I of R such that V (n) = V (Ie), then the topological space X_M is spectral.

• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.369-380
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• 1999

As a continuation of the paper [3], in this paper we investigate the further properties on LI-ideals, and show that how to generate an LI-ideal by both and LI-ideal and an element. We define a prime LI-ideal, and give an equivalent condition for a proper LI-ideal to be prime. Using this result, we establish the extension property and prime LI-ideal theorem.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.315-321
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• 1996

Recently, N. Kehayopulu [4] introduced the concepts of weakly prime ideals of ordered semigroups. In this paper, we define the concepts of left(right) weakly prime and left(right) semiregular. Also we investigate the properties of them.

• Kyungpook Mathematical Journal
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• v.51 no.3
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• pp.339-344
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• 2011

Let D be an integral domain with quotient field K, X be an indeterminate over D, and D[X] be the polynomial ring over D. A prime ideal Q of D[X] is called an upper to zero in D[X] if Q = fK[X] ${\cap}$ D[X] for some f ${\in}$ D[X]. In this paper, we study integral domains D such that every upper to zero in D[X] contains a prime element (resp., a primary element, a t-invertible primary ideal, an invertible primary ideal).

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.277-290
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• 2011

We show that the ${\theta}$-prime radical of a ring R is the set of all strongly ${\theta}$-nilpotent elements in R, where ${\theta}$ is an automorphism of R. We observe some conditions under which the ${\theta}$-prime radical of coincides with the prime radical of R. Moreover we characterize elements in prime radicals of skew Laurent polynomial rings, studying (${\theta}$, ${\theta}^{-1}$)-(semi)primeness of ideals of R.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.7 s.166
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• pp.1120-1128
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• 1999

An elastic-viscoplastic finite element analysis is performed to investigate detailed growth behavior of creep cracks and the numerical results are compared with experimental results. In Cr-Mo steel stress fields obtained from the crack growth method by mesh translation were compared with both cases that the secondary creep rate is only used as creep material property and the primary creep rate is included. Analytical stress fields, Riedel-Rice(RR) field, Hart-Hui-Riedel(HR) field and Prime(named in here) field, and the results obtained by numerical method were evaluated in details. Time vs. stress at crack tip was showed and crack tip stress fields were plotted. These results were compared with analytical stress fields. There is no difference of stress distribution at remote region between the case of 1st creep rate+2nd creep rate and the case of 2nd creep rate only. In case of slow velocity of crack growth, the effect of 1st creep rate is larger than the one of fast crack growth rate. Stress fields at crack tip region we, in order, Prime field, HR field and RR field from crack tip.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1069-1078
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• 2019

Let R be a ring with identity and P(R) denote the prime radical of R. An element r of a ring R is called strongly P-clean, if there exists an idempotent e such that $r-e=p{\in}P$(R) with ep = pe. In this paper, we determine necessary and sufficient conditions for an element of a trivial Morita context to be strongly P-clean.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.2025-2034
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• 2015

In this paper, we characterize some PGL(2, q) by their orders and maximum element orders. We also prove that PSL(2, p) with $p{\geqslant}3$ a prime can be determined by their orders and maximum element orders. Moreover, we show that, in general, if $q=p^n$ with p a prime and n > 1, PGL(2, q) can not be uniquely determined by their orders and maximum element orders. Several known results are generalized.