Semicommutativity of the rings relative to prime radical

Kose, Handan; Üngör, Burcu

doi:10.14712/1213-7243.2015.140

Cited by 2 publications

(3 citation statements)

References 11 publications

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“…Lemma 2.14. ( [5], Lemma 3.2) Let R be a ring and I, J are ideals of R with I ∩ J = 0. Then P (R) = ( i∈I 1 P i ) ( i∈I 2 P i ) and P i is a prime ideal of R for every i ∈ I 1 I 2 where I 1 and I 2 are index sets for the prime ideals of R containing I and J, respectively.…”

Section: R Is Weakly Reversible ([3]mentioning

confidence: 99%

“…Lemma 2.16. ( [5], Lemma 2.17) Let R be a ring and S be a multiplicatively closed subset of R consisting of central regular elements. Then…”

Section: R Is Weakly Reversible ([3]mentioning

confidence: 99%

“…Further contribution to symmetric rings and their generalizations have been made by various authors over the last several years (see, [4], [7], [8], [10]). Recently, semicommutativity of rings related to the prime radical was studied in [5]. This motivated us to introduce rings called P -symmetric rings wherein a ring R is called P -symmetric if for any a, b, c ∈ R, abc = 0 implies bac ∈ P (R).…”

Section: Introductionmentioning

confidence: 99%

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Symmetricity of rings relative to the prime radical

Roy¹,

Subedi²

2020

Preprint

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In this paper, we introduce and study a strict generalization of symmetric rings. We call a ring R 'P -symmetric' if for any a, b, c ∈ R, abc = 0 implies bac ∈ P (R), where P (R) is the prime radical of R. It is shown that the class of P -symmetric rings lies between the class of central symmetric rings and generalized weakly symmetric rings. Relations are provided between P -symmetric rings and some other known classes of rings. From an arbitrary P -symmetric ring, we produce many families of P -symmetric rings.

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Section: R Is Weakly Reversible ([3]mentioning

confidence: 99%

“…Lemma 2.16. ( [5], Lemma 2.17) Let R be a ring and S be a multiplicatively closed subset of R consisting of central regular elements. Then…”

Section: R Is Weakly Reversible ([3]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Symmetricity of rings relative to the prime radical

Roy¹,

Subedi²

2020

Preprint

View full text Add to dashboard Cite

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Symmetricity of rings relative to the prime radical

Roy

Subedi

2022

B Soc Paran Mat

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In this paper, we introduce and study a strict generalization of symmetric rings. We call a ring $R$ \textit{`$P$-symmetric' } if for any $a,\, b,\, c\in R,\, abc=0$ implies $bac\in P(R)$, where $P(R)$ is the prime radical of $R$. It is shown that the class of $P$-symmetric rings lies between the class of central symmetric rings and generalized weakly symmetric rings. Relations are provided between $P$-symmetric rings and some other known classes of rings. From an arbitrary $P$-symmetric ring, we produce many families of $P$-symmetric rings.

show abstract

Semicommutativity of the rings relative to prime radical

Cited by 2 publications

References 11 publications

Symmetricity of rings relative to the prime radical

Symmetricity of rings relative to the prime radical

Symmetricity of rings relative to the prime radical

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