• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.645-652
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• 2002

In this note we investigate some results which concern the types of local rings. In particular it is shown that if the type of a quasi-unmixed local ring A is less than or equal to depth A ＋ 1, and $\hat{A}_p$ is Cohen-Macaulay for every prime $p\neq\hat{m}$, then A is Cohen-Macaulay. (This implies the previously known result: if A satisfies $(S_{n-1})}$, where n is the type of a .ins A, then A is Cohen-Macaulay.)

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1523-1530
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• 2013

Let (A,m) be a Noetherian local ring and M a finitely generated A-module. The notion of pseudo Buchsbaum module was introduced in [3] as an extension of that of Buchsbaum module. In this paper, we give a condition for the idealization A⋉M of M over A to be pseudo Buchsbaum.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.553-563
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• 2017

Different topological dimensions related to the pseudo-prime spectrum of topological modules are studied. An example of topological modules is introduced. Also, we give a result about Noetherianness of the pseudo-prime spectrum of topological modules.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.371-381
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• 2020

A ring R is called right pure-injective if it is injective with respect to pure exact sequences. According to a well known result of L. Melkersson, every commutative Artinian ring is pure-injective, but the converse is not true, even if R is a commutative Noetherian local ring. In this paper, a series of conditions under which right pure-injective rings are either right Artinian rings or quasi-Frobenius rings are given. Also, some of our results extend previously known results for quasi-Frobenius rings.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.9-17
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• 2018

Let $R ={\oplus}_{n{\in}Z}R_n$ be a graded commutative Noetherian ring and let I be a graded ideal of R and J be an arbitrary ideal. It is shown that the i-th generalized local cohomology module of graded module M with respect to the (I, J), is graded. Also, the asymptotic behaviour of the homogeneous components of $H^i_{I,J}(M)$ is investigated for some i's with a specified property.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.653-666
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• 2007

Let R be a commutative Noetherian ring (with a nonzero identity) and let M be an R-module. Further let I be an ideal of R. In this paper, by putting a suitable condition on $Ass_R$(M), we obtain some results concerning $I^{*(M)}$ and prove that the sequence of sets $Ass_R(R/(I^n)^{*(M)})$, $n\;\in\;N$, is increasing and ultimately constant. (Here $(I^n)^{*(M)}$ denotes the integral closure of $I^n$ relative to M.)

• Honam Mathematical Journal
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• v.30 no.1
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• pp.101-113
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• 2008

Let M be an arbitrary module over a commutative Noetherian ring R and let ${\triangle}$ be a multiplicatively closed set of non-zero ideals of R. In this paper, we will introduce the dual notion of ${\triangle}$-closure and ${\triangle}$-dependence of an ideal with respect to M and obtain some related results.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.161-169
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• 2012

Let R be a commutative Noetherian ring and I, J be ideals of R. We introduced the notion of (I; J)-cominimax R-modules. For an integer $n$ and an R-module M, let $H^i_{I,J}(M)$ be an (I; J)-cominimax R-module for all $i<n$. The J-minimaxness of some Ext modules of $H^n_{I,J}(M)$ is investigated. Among of the obtaining results, there is a generalization of the main result of [1].

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.255-277
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• 2006

By means of the use of a triangular norm T, the notion of T-fuzzy hyperideals in hypernear-rings is stated, and basic properties are investigated. Moreover, the notion of Noetherian hypernear-rings is introduced, and its characterization is given. At last, the properties of quotient hypernear-rings and T-fuzzy characteristic hyper ideals are discussed.

• The Pure and Applied Mathematics
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• v.7 no.1
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• pp.33-40
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• 2000

We prove some characterization of rings with chain conditions in terms of fuzzy quotient rings and fuzzy ideals. We also show that a ring R is left Artinian if and only of the set of values of every fuzzy ideal on R is upper well-ordered.