• 대한수학회보
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• 제40권1호
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• pp.167-176
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• 2003

In [3］, Del Valle, Enochs and Martinez studied flat envelopes over rings and they showed that over rings as in the title these are very well behaved. If we replace flat with injective and envelope with the dual notion of a cover we then have the injective covers. In this article we show that these injective covers over the commutative noetherian rings with global dimension at most 2 have properties analogous to those of the flat envelopes over these rings.

• 대한수학회지
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• 제55권6호
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• pp.1499-1512
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• 2018

Recently, Anderson and Dumitrescu's S-finiteness has attracted the interest of several authors. In this paper, we introduce the notions of S-finitely presented modules and then of S-coherent rings which are S-versions of finitely presented modules and coherent rings, respectively. Among other results, we give an S-version of the classical Chase's characterization of coherent rings. We end the paper with a brief discussion on other S-versions of finitely presented modules and coherent rings. We prove that these last S-versions can be characterized in terms of localization.

• Kyungpook Mathematical Journal
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• 제54권4호
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• pp.595-606
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• 2014

In this paper three more right Jacobson-type radicals, $J^r_{g{\nu}}$, are introduced for near-rings which generalize the Jacobson radical of rings, ${\nu}{\in}\{0,1,2\}$. It is proved that $J^r_{g{\nu}}$ is a special radical in the class of all near-rings. Unlike the known right Jacobson semisimple near-rings, a $J^r_{g{\nu}}$-semisimple near-ring R with DCC on right ideals is a direct sum of minimal right ideals which are right R-groups of type-$g_{\nu}$, ${\nu}{\in}\{0,1,2\}$. Moreover, a finite right $g_2$-primitive near-ring R with eRe a non-ring is a near-ring of matrices over a near-field (which is isomorphic to eRe), where e is a right $g_2$-primitive idempotent in R.

• Kyungpook Mathematical Journal
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• 제47권3호
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• pp.363-372
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• 2007

An element $a$ in a ring R is called left morphic if $$R/Ra{\simeq_-}1(a)$$. A ring is called left morphic if every element is left morphic. In this paper, an element $a$ in a ring R is called left ${\pi}$-morphic (resp. left G-morphic) if there exists a positive number $n$ such that $a^n$ (resp. $a^n{\neq}0$) is left morphic. A ring R is called left ${\pi}$-morphic (resp. left G-morphic) if every element is left ${\pi}$-morphic (resp. left G-morphic). The Morita invariance of left ${\pi}$-morphic (resp. left G-morphic) rings is discussed. Several relevant properties are proved. In particular, it is shown that a left Noetherian ring R with $M_4(R)$ left G-morphic or $M_2(R)$ left morphic is QF. Some known results of left morphic rings are extended to left G-morphic rings and left ${\pi}$-morphic rings.

• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.397-406
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• 2013

A ring R is called a left (right) SF-ring if simple left (right) R-modules are flat. It is still unknown whether a left (right) SF-ring is von Neumann regular. In this paper, we give some conditions for a left (right) SF-ring to be (a) von Neumann regular; (b) strongly regular; (c) division ring. It is proved that: (1) a right SF-ring R is regular if maximal essential right (left) ideals of R are weakly left (right) ideals of R (this result gives an affirmative answer to the question raised by Zhang in 1994); (2) a left SF-ring R is strongly regular if every non-zero left (right) ideal of R contains a non-zero left (right) ideal of R which is a W-ideal; (3) if R is a left SF-ring such that $l(x)(r(x))$ is an essential left (right) ideal for every right (left) zero divisor x of R, then R is a division ring.

• Kyungpook Mathematical Journal
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• 제48권1호
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• pp.143-154
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• 2008

Lomp [9] has studied finitely generated projective modules over semilocal rings. He obtained the following: finitely generated projective modules over semilocal rings are semilocal. We shall give necessary and sufficient conditions for finitely generated modules to be semilocal modules. By using a lifting property, we also give characterizations of right perfect (semiperfect) rings. Our main results can be summarized as follows: (1) Let M be a finitely generated module. Then M has finite hollow dimension if and only if M is weakly supplemented if and only if M is semilocal. (2) A ring R is right perfect if and only if every flat right R-module is lifting and every right R-module has a flat cover if and only if every quasi-projective right R-module is lifting. (3) A ring R is semiperfect if and only if every finitely generated flat right R-module is lifting if and only if RR satisfies the lifting property for simple factor modules.

• 대한기계학회논문집A
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• 제26권10호
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• pp.2211-2218
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• 2002

In this study, an optimal design study has been made to determine dimensions of die and multi stress rings for extrusion process. For this purpose, a thermo-rigid-viscoplastic finite element program, CAMPform, was used fur forming analysis of extrusion process and a developed elastic finite element program fur elastic stress analysis of the die set including stress rings. And an optimization program, DOT, was employed for the optimization analysis. From this investigation, it was found out that the amount of shrink fitting incurred by the order of assembly of the die set should be taken into account for optimization when the multi stress rings are used in practice. In addition, it is construed that the proposed design method can be beneficial fur improving the tool life of cold extrusion die set.

• Korean Journal of Mathematics
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• 제27권1호
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• pp.141-150
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• 2019

In this article we investigate the structure of rings in which lower nilradicals coincide with upper nilradicals. Such rings shall be said to be quasi-2-primal. It is shown first that the $K{\ddot{o}}the^{\prime}s$ conjecture holds for quasi-2-primal rings. So the results in this article may provide interesting and useful information to the study of nilradicals in various situations. In the procedure we study the structure of quasi-2-primal rings, and observe various kinds of quasi-2-primal rings which do roles in ring theory.

• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.711-721
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• 2020

The concepts of an Amitsur ring and a hereditary Amitsur ring, which were introduced and studied by S. Tumurbat in a recent paper, are generalized. For a positive integer n, a ring A is said to be an n-Amitsur ring if γ(A[Xn]) = (γ(A[Xn]) ∩ A)[Xn] for all radicals γ, where A[Xn] is the polynomial ring over A in n commuting indeterminates. If a ring A satisfies the above equation for all hereditary radicals γ, then A is said to be a hereditary n-Amitsur ring. Characterizations and examples of these rings are provided. Moreover, new radicals associated with n-Amitsur rings are introduced and studied. One of these is a special radical and its semisimple class is polynomially extensible.

• Kyungpook Mathematical Journal
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• 제62권2호
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• pp.213-227
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• 2022

We discuss the relation between units and nilpotents of a ring, concentrating on the transitivity of units on nilpotents under regular group actions. We first prove that for a ring R, if U(R) is right transitive on N(R), then Köthe's conjecture holds for R, where U(R) and N(R) are the group of all units and the set of all nilpotents in R, respectively. A ring is called right UN-transitive if it satisfies this transitivity, as a generalization, a ring is called unilpotent-IFP if aU(R) ⊆ N(R) for all a ∈ N(R). We study the structures of right UN-transitive and unilpotent-IFP rings in relation to radicals, NI rings, unit-IFP rings, matrix rings and polynomial rings.