• East Asian mathematical journal
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• v.17 no.2
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• pp.275-286
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• 2001

In this paper, a skew polynomial ring $R[x;\alpha]$ of a ring R with a monomorphism $\alpha$ are investigated as follows: For a reduced ring R, assume that $\alpha(P){\subseteq}P$ for any minimal prime ideal P in R. Then (i) $R[x;\alpha]$ is a reduced ring, (ii) a ring R is Baer(resp. quasi-Baer, p.q.-Baer, a p.p.-ring) if and only if the skew polynomial ring $R[x;\alpha]$ is Baer(resp. quasi-Baer, p.q.-Baer, a p.p.-ring).

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.31-47
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• 2020

In this paper, we discuss in detail some of the properties of the new kind of (∈, ∈ ∨q)-fuzzy ideals in Near-ring. The concept of (∈, ∈ ∨q^δ₀)-fuzzy ideal of Near-ring is introduced and some of its related properties are investigated.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.1-12
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• 2018

We introduce the notion of ordered intra k-regular semirings, characterize them using their ordered k-ideals and prove that an ordered semiring S is both ordered k-regular and ordered intra k-regular if and only if every ordered quasi k-ideal or every ordered k-bi-ideal of S is ordered k-idempotent.

• Kyungpook Mathematical Journal
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• v.26 no.2
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• pp.149-155
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• 1986

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.545-558
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• 2017

In this paper, we introduce generalised quasi-ideals in ordered ternary semigroups. Also, we define ordered m-right ideals, ordered (p, q)-lateral ideals and ordered n-left ideals in ordered ternary semigroups and studied the relation between them. Some intersection properties of ordered (m,(p, q), n)-quasi ideals are examined. We also characterize these notions in terms of minimal ordered (m,(p, q), n)-quasi-ideals in ordered ternary semigroups. Moreover, m-right simple, (p, q)-lateral simple, n-left simple, and (m,(p, q), n)-quasi simple ordered ternary semigroups are defined and some properties of them are studied.

• East Asian mathematical journal
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• v.38 no.1
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• pp.1-12
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• 2022

Let R be a ring with an endomorphism σ and a σ-derivation δ. R is called (σ, δ)-Baer (resp. (σ, δ)-quasi-Baer, (σ, δ)-p.q.-Baer, (σ, δ)-p.p.) if the right annihilator of every right (σ, δ)-set (resp., (σ, δ)-ideal, principal (σ, δ)-ideal, (σ, δ)-element) of R is generated by an idempotent of R. In this paper, for a given Ore extension A = R[x; σ, δ] of R, the following properties are investigated: If R is a σ-rigid ring in which σ and δ commute, then (1) R is (σ, δ)-Baer if and only if R is (σ, δ)-quasi-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-quasi-Baer; (2) R is (σ, δ)-p.p. if and only if R is (σ, δ)-p.q.-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.p. if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.q.-Baer.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.121-122
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• 2023

In this erratum, we correct a mistake in the proof of Proposition 2.7. In fact the equivalence (3) ⇐ (4) "R is a quasi-regular ring if and only if R is a reduced ring and every principal ideal contained in Z(R) is a 0-ideal" does not hold as we only have Rx ⊆ O(S).

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.69-75
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• 1997

• East Asian mathematical journal
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• v.34 no.3
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• pp.305-316
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• 2018

Let R be a ring with identity. A right ideal ideal I of a ring R is called ref lexive (resp. completely ref lexive) if $aRb{\subseteq}I$ implies that $bRa{\subseteq}I$ (resp. if $ab{\subseteq}I$ implies that $ba{\subseteq}I$) for any $a,\;b{\in}R$. R is called ref lexive (resp. completely ref lexive) if the zero ideal of R is a reflexive ideal (resp. a completely reflexive ideal). Let K(R) (called the ref lexive radical of R) be the intersection of all reflexive ideals of R. In this paper, the following are investigated: (1) Some equivalent conditions on an reflexive ideal of a ring are obtained; (2) reflexive (resp. completely reflexive) property is Morita invariant; (3) For any ring R, we have $K(M_n(R))=M_n(K(R))$ where $M_n(R)$ is the ring of all n by n matrices over R; (4) For a ring R, we have $K(R)[x]{\subseteq}K(R[x])$; in particular, if R is quasi-Armendaritz, then R is reflexive if and only if R[x] is reflexive.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.123-135
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• 2023

It is proved that there is a one to one correspondence between representations of C^*-ternary ring M and C^*-algebra 𝒜(M). We discuss primitive and modular ideals of a C^*-ternary ring and prove that a closed ideal I is primitive or modular if and only if so is the ideal 𝒜(I) of 𝒜(M). We also show that a closed ideal in M is primitive if and only if it is the kernel of some irreducible representation of M. Lastly, we obtain approximate identity characterization of strongly quasi-central C^*-ternary ring and the ideal structure of the TRO V ⊗^tmin B for a C^*-algebra B.