On Unit-Central Rings

Khurana, Dinesh; Marks, Greg; Srivastava, Ashish K.

doi:10.1007/978-3-0346-0286-0_13

Cited by 11 publications

(6 citation statements)

References 27 publications

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“…By M. P. Darzin [12] a ring R is a CN -ring whenever every nilpotent element of R is central. D. Khurana et al [33], introduced the notion of unit-central rings (i.e., every invertible element of it lies in center), and show that each unit-central ring is a CN -ring. It is clear that CN -rings and reversible rings are nil-reversible.…”

Section: Lemma 25 ([19 Theorem 44])mentioning

confidence: 99%

On Annihilations of Ideals in Skew Monoid Rings

Mohammadi¹,

Moussavi²,

Zahiri³

2016

Journal of the Korean Mathematical Society

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Abstract. According to Jacobson [31], a right ideal is bounded if it contains a non-zero ideal, and Faith [15] called a ring strongly right bounded if every non-zero right ideal is bounded. From [30], a ring is strongly right AB if every non-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy Property (A) and the conditions asked by Nielsen [42]. It is shown that for a u.p.-monoid M and σ : M → End(R) a compatible monoid homomorphism, if R is reversible, then the skew monoid ring R * M is strongly right AB. If R is a strongly right AB ring, M is a u.p.-monoid and σ : M → End(R) is a weakly rigid monoid homomorphism, then the skew monoid ring R * M has right Property (A).

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Section: Lemma 25 ([19 Theorem 44])mentioning

confidence: 99%

On Annihilations of Ideals in Skew Monoid Rings

Mohammadi¹,

Moussavi²,

Zahiri³

2016

Journal of the Korean Mathematical Society

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“…Commutative rings and reduced rings are central reduced. Every unitcentral ring (i.e., every unit element of R is central [13]) is central reduced.…”

Section: Central Reduced Ringsmentioning

confidence: 99%

Rings in which every nilpotent is central

Ungor,

Halicioglu,

Kose

et al. 2013

Preprint

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“…According to [3], a ring R is called weakly semicommutative if for any w, h ∈ R, wh = 0 implies wrh ∈ N (R) for any r ∈ R. Clearly, weakly semicommutative rings are generalizations of semicommutative rings. Following [19], R is called unit-central whenever U (R) ⊆ Z(R).…”

Section: Introductionmentioning

confidence: 99%

Nil-reversible rings

Subba,

Subedi

2021

Preprint

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This paper introduces and studies nil-reversible rings wherein we call a ring R nil-reversible if the left and right annihilators of every nilpotent element of R are equal. Reversible rings (and hence reduced rings) form a proper subclass of nil-reversible rings and hence we provide some conditions for a nil-reversible ring to be reduced. It turns out that nil-reversible rings are abelian, 2-primal, weakly semicommutative and nil-Armendariz. Further, we observe that the polynomial ring over a nil-reversible ring R is not necessarily nil-reversible in general, but it is nil-reversible if R is Armendariz additionally.

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On Unit-Central Rings

Cited by 11 publications

References 27 publications

On Annihilations of Ideals in Skew Monoid Rings

On Annihilations of Ideals in Skew Monoid Rings

Rings in which every nilpotent is central

Nil-reversible rings

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