On Rings Whose Strongly Prime Ideals Are Completely Prime

Kaplansky introduced the concept of the K-rings, concerning the commutativity of rings. In this paper, we concentrate on a property of K-rings, introducing the concept of the strongly NI rings, which is stronger than NI-ness. We first examine the relations among the concepts concerned with K-rings and strongly NI rings, constructing necessary examples in the process. We also show that strong NI-ness is a hereditary radical property.

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On a Hereditary Radical Property Relating to the Reducedness

Communications in Algebra ◽

10.1080/00927871003597626 ◽

2011 ◽

Vol 39 (2) ◽

pp. 608-620 ◽

Cited By ~ 2

Author(s):

Cheong Mi Ha ◽

Chan Huh ◽

Hong Kee Kim ◽

Nam Kyun Kim ◽

Yang Lee

Keyword(s):

Hereditary Radical ◽

Radical Property

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N-ideals of commutative rings

Filomat ◽

10.2298/fil1710933t ◽

2017 ◽

Vol 31 (10) ◽

pp. 2933-2941 ◽

Cited By ~ 3

Author(s):

Unsal Tekir ◽

Suat Koc ◽

Kursat Oral

Keyword(s):

Commutative Ring ◽

Commutative Rings ◽

Proper Ideal ◽

Prime Ideals ◽

Nonzero Identity

In this paper, we present a new classes of ideals: called n-ideal. Let R be a commutative ring with nonzero identity. We define a proper ideal I of R as an n-ideal if whenever ab ? I with a ? ?0, then b ? I for every a,b ? R. We investigate some properties of n-ideals analogous with prime ideals. Also, we give many examples with regard to n-ideals.

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On $$\phi $$-1-absorbing prime ideals

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry ◽

10.1007/s13366-020-00557-w ◽

2021 ◽

Author(s):

Eda Yildiz ◽

Unsal Tekir ◽

Suat Koc

Keyword(s):

Prime Ideals

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Correction to: Prime ideals and generalized derivations with central values on rings

Rendiconti del Circolo Matematico di Palermo (1952 -) ◽

10.1007/s12215-020-00583-6 ◽

2020 ◽

Author(s):

Mamouni Abdellah ◽

Oukhtite Lahcen ◽

Zerra Mohammed

Keyword(s):

Prime Ideals ◽

Generalized Derivations ◽

Central Values

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Kurosh-Amitsur Right Jacobson Radical of Type 0 for Right Near-Rings

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2008/741609 ◽

2008 ◽

Vol 2008 ◽

pp. 1-6

Author(s):

Ravi Srinivasa Rao ◽

K. Siva Prasad ◽

T. Srinivas

Keyword(s):

Jacobson Radical ◽

Paper Properties ◽

Hereditary Radical ◽

Constant Part ◽

The Right

By a near-ring we mean a right near-ring.J0r, the right Jacobson radical of type 0, was introduced for near-rings by the first and second authors. In this paper properties of the radicalJ0rare studied. It is shown thatJ0ris a Kurosh-Amitsur radical (KA-radical) in the variety of all near-ringsR, in which the constant partRcofRis an ideal ofR. So unlike the left Jacobson radicals of types 0 and 1 of near-rings,J0ris a KA-radical in the class of all zero-symmetric near-rings.J0ris nots-hereditary and hence not an ideal-hereditary radical in the class of all zero-symmetric near-rings.

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