• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.425-436
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• 2022

In this paper we introduce the notion of 2-absorbing primary ideals of a commutative semigroup. We establish the relations between 2-absorbing primary ideals and prime, maximal, semiprimary and 2-absorbing ideals. We obtain various characterization theorems for commutative semigroups in which 2-absorbing primary ideals are prime, maximal, semiprimary and 2-absorbing ideals. We also study some other important properties of 2-absorbing primary ideals of a commutative semigroup.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.331-340
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• 2023

In this paper, the concept of a maximal chain of ideals is introduced. Some properties of such chains are studied. We introduce some other concepts related to a maximal chain of ideals such as the n-maximal ideal, the maximal dimension of a ring S (M. dim(S)), the maximal depth of an ideal K of S (M.d(K)) and maximal height of an ideal K(M.d(K)).

• Kyungpook Mathematical Journal
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• v.63 no.4
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• pp.571-575
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• 2023

Let D be an integral domain and let * be a star-operation on D. In this article, we give new characterizations of *_w-Noetherian domains and *_w-principal ideal domains. More precisely, we show that D is a *_w-Noetherian domain (resp., *_w-principal ideal domain) if and only if every *_w-countable type ideal of D is of *_w-finite type (resp., principal).

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.701-708
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• 2012

The notion of an enlarged $p$-ideal and a fuzzy $p$-ideal in BCI-algebras with degree are introduced. Related properties of them are investigated.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.739-746
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• 2010

In this short paper, we show that properties of an ideal I of a ring R are related to those of the homogeneous ideal I(+)IM of a ring R(+)M.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.507-511
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• 1997

In this paper, we give the characterizations of right(left) semiregular $po$-semigroups using the notions of some type ideals.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.783-787
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• 1995

In this paper we characterize cancellation ideals in terms of multiplication ideals. Especially, we find a condition for an ideal generated by three elements to be a cancellation ideal.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.465-475
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• 2012

We characterize the fuzzy ideal generated by a fuzzy subset in a semigroup and the fuzzy interior ideal generated by a fuzzy subset in a semigroup. Our work generalizes the characterizations ([8]) of those fuzzy ideals generated by fuzzy subsets in semigroups with an identity element.

• Korean Journal of Mathematics
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• v.7 no.1
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• pp.111-116
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• 1999

In this paper, we introduce the concepts of quasi retract ideals and quasi retract topological semigroups which are weaker than those of retract ideals and retract topological semigroups, respectively. We prove that every $n$-th power ideal of a commutative power cancellative power ideal topological semigroup is a quasiretract ideal.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.403-412
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• 2008

We define the operations ${\vee}$ and ${\wedge}$ for fuzzy sets in a lattice, characterize fuzzy sublattices in terms of ${\vee}$ and ${\wedge}$, develop some properties of the distributive fuzzy sublattices, and find the fuzzy ideal generated by a fuzzy subset in a lattice and the fuzzy dual ideal generated by a fuzzy subset in a lattice.