Structures paragraduées (groupes, anneaux, modules), I

Krasner, Marc; Vuković, Mirjana

doi:10.3792/pjaa.62.350

Cited by 8 publications

(7 citation statements)

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“…Such a structure is named anneid [3,8,22] and an origin of this approach goes back to [21]. For a survey on anneids, one may also consult [23,31]. Everything obtained for anneids holds for S-graded rings inducing S and vice versa.…”

Section: Preliminariesmentioning

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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Section: Preliminariesmentioning

confidence: 99%

On graded nil clean rings

Ilić-Georgijević

Şahinkaya

2018

Communications in Algebra

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“…Then there exists an upper bound for all δ(x), x ∈ A; vi) G is generated by H with the set of H-internal and left commutation relations (see [7]). …”

Section: Remark 13mentioning

confidence: 99%

“…If we put ζ = ξη, we will get ∆-multiplication and we call it minimal multiplication ( [7] ([7]). This multiplication is called minimal multiplication.…”

Section: Theorem 14 ([7]) Every Extragraded Group Is a Paragraded Gmentioning

confidence: 99%

“…This group is a paragraded group, since HOM(M, M ′ ) is a homogeneous subgroup of hom(M, M ′ ), and hom(M, M ′ ) is a paragraded group according to [7]. Remark 2.7.…”

Section: Lemma 25 Let G G ′ Be Commutative Paragraded Groups Of Tymentioning

confidence: 99%

“…Actually, from the homogeneous point of view, a multigroupoid does not have to be a homogroupoid ( [7]). Paragraded groups are defined in [7] by the six-axiom system as follows. …”

Section: Introductionmentioning

confidence: 99%

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On the categories of paragraded groups and modules of type Δ

Georgijević¹

2012

SJM

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Abstract. In this paper we observe the categories of paragraded groups and R-modules with respect to the same set of grades ∆, where R is the paragraded ring with the set of grades ∆. We turn our attention to constructing new objects in those categories using the sets of morphisms of grade δ ∈ ∆. This process defines bifunctors which happen to be left exact. Thus we may construct the right derived functor and it turns out that it behaves the same as in the case of the category of abstract modules.

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Paragraded Rings and Their Ideals

Vuković

Ilić-Georgijević

2013

J Math Sci

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Structures paragraduées (groupes, anneaux, modules), I

Cited by 8 publications

References 1 publication

On graded nil clean rings

On graded nil clean rings

On the categories of paragraded groups and modules of type Δ

Paragraded Rings and Their Ideals

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