On generators of Peiffer ideal of a pre-$-algebroid in a precrossed module and applications

Akça, İbrahim İlker; Avcıoğlu, Osman

doi:10.20852/ntmsci.2017.225

Cited by 3 publications

(1 citation statement)

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“…The method we use throughout this paper is similar to that used for coproduct of crossed P-modules in [4]. We must also state that the generators in (1) and (2) are special types of Pei er commutators and we've shown in [1] that the ideals I M*N and I M N are, in fact, Pei er ideals of M * N and M N, respectively.…”

Section: Introductionmentioning

confidence: 99%

Coproduct of Crossed A-Modules of R-Algebroids

Avcıoğlu

Akça

2017

Topological Algebra and Its Applications

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Abstract:In this study we construct, in the category XAlg(R) /A of crossed A-modules of R-algebroids, the coproduct of given two crossed A-modules M = (µ : M −→ A) and N = (η : N −→ A) of R-algebroids in two di erent ways: Firstly we construct the coproduct M • * N by using the free product M * N of pre-R-algebroids M and N, and then we construct the coproduct M • N by using the semidirect product M N of M and N via µ. Finally we construct an isomorphism between M • * N and M • N.

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Section: Introductionmentioning

confidence: 99%

Coproduct of Crossed A-Modules of R-Algebroids

Avcıoğlu

Akça

2017

Topological Algebra and Its Applications

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Split (Pre)crossed Modules over $R$-Algebroids

Avcıoğlu

2024

TJMCS

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In this paper, we introduce (d-)split and (d-)split$^{+}$ epimorphisms and (d-)split and d-split$^{\ast}$ (pre)crossed modules in the context of algebroids. Moreover, we examine their categorical properties, and in particular, we give a necessary and sufficient condition for a morphism of pre-$R$-algebroids to be a d-split precrossed module and a necessary and sufficient condition for a d-split$^{\ast}$ precrossed module to be a crossed module. In addition, we examine the hierarchical relations between the categories obtained and look over some results for split (pre)crossed modules over associative $R$-algebras, as a reduced case.

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Bimultipliers of R-algebroids

Kahrıman

2024

Ikonion Journal of Mathematics

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Group action is determined bythe automorphism group and algebra action is defined by the multiplication algebra. In the study we generalize the multiplication algebra by defining multipliers of an R-algebroid M. Firstly, the set of bimultipliers on an R-algebroid is introduced, it is denoted by Bim(M), then it is proved that this set is an R-algebroid, it is called multiplication R-algebroid. Using this Bim(M), for an R-algebroid morphism A → Bim(M) it is shown that this morphism gives an R-algebroid action. Then we examine some of the properties associated with this action.

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On generators of Peiffer ideal of a pre-$-algebroid in a precrossed module and applications

Cited by 3 publications

References 10 publications

Coproduct of Crossed A-Modules of R-Algebroids

Coproduct of Crossed A-Modules of R-Algebroids

Split (Pre)crossed Modules over $R$-Algebroids

Bimultipliers of R-algebroids

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