• East Asian mathematical journal
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• 제16권1호
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• pp.33-48
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• 2000

In this paper, for any ring R with an identity, in order to study prime ideals of the endomorphism ring $End_R$(M) of left R-module $_RM$, meet-prime submodules, prime radical, sum-prime submodules and the prime socle of a module are defined. Some relations of the prime radical, the prime socle of a module and the prime radical of the endomorphism ring of a module are investigated. It is revealed that meet-prime(or sum-prime) modules and semi-meet-prime(or semi-sum-prime) modules have their prime, semi-prime endomorphism rings, respectively.

• 호남수학학술지
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• 제23권1호
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• pp.1-4
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• 2001

In [2, 7.3.2], the set of attached prime ideals of local cohomology module $H_m^n(M)$ were calculated, where (A, m) be Noetherian local ring, M finite A-module and $dim_A(M)=n$, and also in the special case in which furthermore A is a homomorphic image of a Gornestien local ring (A', m') (see [2, 11.3.6]). In this paper, we shall obtain this set, by another way in this special case.

• 대한수학회논문집
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• 제27권4호
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• pp.645-651
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• 2012

Based on a sub-BCK-algebra K of a BCI-algebra X, the notions of N-subalgebras and N-ideals of X are introduced, and their relations/properties are investigated.

• 호남수학학술지
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• 제28권4호
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• pp.471-484
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• 2006

The notion of ideals in WFI-algebras is introduced, and several properties are investigated. Relations between a filter and an ideal are given, and characterizations of an ideal are provided. An extension property for an ideal is established.

• 호남수학학술지
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• 제28권4호
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• pp.499-511
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• 2006

It is well-known that every finitely generated torsion-free module over a principal ideal domain is free. This will be generalized. We deal with ideals of the finite, external direct product of certain rings. Finally, if M is a torsion-free, finitely generated module over a reduced, Noetherian ring A, then we prove that Ms is a projective module over As, where $S=A{\setminus}(A)$.

• 호남수학학술지
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• 제30권2호
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• pp.379-390
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• 2008

More general forms of a BZ-ideal and a T-ideal are given, and appropriate examples are provided. The notion of T(m)-type BZ-algebra is introduced, and its characterizations are given.

• 대한수학회보
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• 제40권3호
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• pp.503-508
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• 2003

We prove that every M-ideal is strongly proximinal and that, for any Banach space X, $K(X,\;c_0)$ is an M-ideal in $L(X,\;\ell^{\infty})$.

• 대한수학회논문집
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• 제23권4호
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• pp.487-497
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• 2008

Buchsbaum and Eisenbud showed that every Gorenstein ideal of grade 3 is generated by the submaximal order pfaffians of an alternating matrix. In this paper, we describe a method for constructing a class of type 3, grade 3, perfect ideals which are not Gorenstein. We also prove that they are algebraically linked to an even type grade 3 almost complete intersection.

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.251-259
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• 2002

The fuzzification of an ideal in a Lie algebra is considered. Using a level subset of a fuzzy subset of a Lie algebra, we give a characterization of a fuzzy ideal, and using a family of ideals of a Lie algebra, we establish a fuzzy ideal. With relation to the ascending chain of ideals, a characterization for the set of values of any fuzzy ideal to be a well-ordered subset of the closed unit interval [0,1] is stated.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1489-1500
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• 2011

The notions of $\mathcal{N}$-subalgebra, (positive implicative) $\mathcal{N}$-ideals of d-algebras are introduced, and related properties are investigated. Characterizations of an $\mathcal{N}$-subalgebra and a (positive implicative) $\mathcal{N}$-ideals of d-algebras are given. Relations between an $\mathcal{N}$-subalgebra, an $\mathcal{N}$-ideal and a positive implicative N-ideal of d-algebras are discussed.