On graded Thierrin radicals of graded rings

Ilić-Georgijević, Emil

doi:10.1080/00927872.2016.1248243

Cited by 10 publications

(3 citation statements)

References 12 publications

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“…We do not recall these notions here since we only need their properties. For more information on these and related radicals, one may also consult [11,12,13].…”

Section: Graded Nil Clean Ringsmentioning

confidence: 99%

On graded nil clean rings

Ilić-Georgijević

Şahinkaya

2018

Communications in Algebra

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In this paper we introduce and study the notion of a graded (strongly) nil clean ring which is group graded. We also deal with extensions of graded (strongly) nil clean rings to graded matrix rings and to graded group rings. The question of when nil cleanness of the component, which corresponds to the neutral element of a group, implies graded nil cleanness of the whole graded ring is examined. Similar question is discussed in the case of groupoid graded rings as well.

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“…We do not recall these notions here since we only need their properties. For more information on these and related radicals, one may also consult [11,12,13].…”

Section: Graded Nil Clean Ringsmentioning

confidence: 99%

On graded nil clean rings

Ilić-Georgijević

Şahinkaya

2018

Communications in Algebra

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“…These represent generalizations of results obtained in [8,9] for the graded Jacobson radical of a graded ring to the case of homogeneous semigroups. For all the notions related to semigroup theory which are not included in this article, we refer to [3,4] and [29], and for the notions related to graded rings, see [13,21,23].…”

Section: Definition 11 ([21 23])mentioning

confidence: 99%

On the Jacobson and simple radicals of semigroups

Ilić-Georgijević

2018

Filomat

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“…The graded prime radical of R, denoted by P g (R), is defined as the intersection of all graded prime ideals of R (see [8]). For the graded versions of other classical radicals of rings, see [9,10,11]. This graded ring construction is too technical to present all of the details here.…”

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confidence: 99%

On Graded Uj-Rings

Ilić-Georgijević¹

2020

International Electronic Journal of Algebra

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In this paper, graded rings are S-graded rings inducing S, that is, rings whose additive groups can be written as a direct sum of a family of their additive subgroups indexed by a nonempty set S, and such that the product of two homogeneous elements is again a homogeneous element. As a generalization of the recently introduced notion of a U J-ring, we define a graded U J-ring. Graded nil clean rings which are graded U J are described. We also investigate the graded U J-property under some graded ring constructions.

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On graded Thierrin radicals of graded rings

Cited by 10 publications

References 12 publications

On graded nil clean rings

On graded nil clean rings

On the Jacobson and simple radicals of semigroups

On Graded Uj-Rings

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