Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Sayı: 35, 72 - 90, 30.06.2021
https://doi.org/10.53570/jnt.905298

Öz

Kaynakça

  • S. M. Lane, Extensions and Obstructions for Rings, Illinois Journal of Mathematics 121 (1958) 316-345.
  • J. H. C. Whitehead, Combinatorial Homotopy I, Bulletin of the American Mathematical Society 55 (1949) 231-245.
  • J. H. C. Whitehead, Combinatorial Homotopy II, Bulletin of the American Mathematical Society 55 (1949) 453-456.
  • S. Lichtenbaum, M. Schlessinger, The Cotangent Complex of a Morphism, Transactions of the American Mathematical Society 128(1) (1967) 41-70.
  • M. Gerstenhaber, On the Deformation of Rings and Algebras: II, Annals of Mathematics 84(1) (1966) 1-19.
  • P. Dedecker, A. S. T. Lue, A Nonabelian Two-Dimensional Cohomology for Associative Algebras, Bulletin of the American Mathematical Society 72(6) (1966) 1044-1050. K. J. Norrie, Actions and Automorphisms of Crossed Modules, Bulletin de la Société Mathématique de France 118 (1990) 129-146.
  • A. S. T. Lue, Semi-Complete Crossed Modules and Holomorp hs of Groups, Bulletin of the London Mathematical Society 11 (1979) 8-16.
  • Z. Arvasi, U. Ege, Annihilators, Multipliers and Crossed Modules, Applied Categorical Structures 11 (2003) 487-506.
  • S. Hürmetli, Bimultiplication of Crossed Modules, PhD Dissertation, Eskişehir Osmangazi University, (2016) Eskişehir, Turkey.
  • Y. Boyacı, J. M. Casas, T. Datuashvili, E. Ö. Uslu, Actions in Modified Categories of Interest with Application Crossed Modules, Theory and Applications of Categories 30(25) (2015) 882-908.
  • G. J. Ellis, Higher Dimensional Crossed Modules of Algebras, Journal of Pure and Applied Algebra 52(3) (1988) 277-282.
  • A. S. -T. Lue, Non-Abelian cohomology of Associative Algebras, The Quarterly Journal of Mathematics 19(1) (1968) 159-180.
  • R. Lavendhomme, Th. Lucas, On Modules and Crossed Modules, Journal of Algebra 179 (1996) 936-963.
  • Z. Arvasi. Crossed Squares and 2-Crossed Modules of Commutative Algebras, Theory and Applications of Categories 3(7) (1997) 160-181.
  • Z. Arvasi, E. Ulualan, Homotopical Aspects of Commutative Algebras I: Freeness Conditions for Crossed Squares, Journal of Homotopy and Related Structure 10 (2013) 495-518.
  • E. S. Yılmaz, K. Yılmaz, On Crossed Squares of Commutative Algebras, Mathematical Sciences and Applications E-Notes (8) 2 (2020) 32-41.

Bimultiplications and Annihilators of Crossed Modules in Associative Algebras

Yıl 2021, Sayı: 35, 72 - 90, 30.06.2021
https://doi.org/10.53570/jnt.905298

Öz

In this paper, we present a generalization of the concept of the bimultiplication algebra by defining the bimultiplication of crossed modules in associative algebras. Using this structure, we construct the actor of a crossed module in associative algebras, and we obtain annihilators of crossed modules as the kernel of a crossed module morphism from a crossed module to its actor. Moreover, we construct a link between this morphism and a crossed square, two-dimensional crossed module.

Kaynakça

  • S. M. Lane, Extensions and Obstructions for Rings, Illinois Journal of Mathematics 121 (1958) 316-345.
  • J. H. C. Whitehead, Combinatorial Homotopy I, Bulletin of the American Mathematical Society 55 (1949) 231-245.
  • J. H. C. Whitehead, Combinatorial Homotopy II, Bulletin of the American Mathematical Society 55 (1949) 453-456.
  • S. Lichtenbaum, M. Schlessinger, The Cotangent Complex of a Morphism, Transactions of the American Mathematical Society 128(1) (1967) 41-70.
  • M. Gerstenhaber, On the Deformation of Rings and Algebras: II, Annals of Mathematics 84(1) (1966) 1-19.
  • P. Dedecker, A. S. T. Lue, A Nonabelian Two-Dimensional Cohomology for Associative Algebras, Bulletin of the American Mathematical Society 72(6) (1966) 1044-1050. K. J. Norrie, Actions and Automorphisms of Crossed Modules, Bulletin de la Société Mathématique de France 118 (1990) 129-146.
  • A. S. T. Lue, Semi-Complete Crossed Modules and Holomorp hs of Groups, Bulletin of the London Mathematical Society 11 (1979) 8-16.
  • Z. Arvasi, U. Ege, Annihilators, Multipliers and Crossed Modules, Applied Categorical Structures 11 (2003) 487-506.
  • S. Hürmetli, Bimultiplication of Crossed Modules, PhD Dissertation, Eskişehir Osmangazi University, (2016) Eskişehir, Turkey.
  • Y. Boyacı, J. M. Casas, T. Datuashvili, E. Ö. Uslu, Actions in Modified Categories of Interest with Application Crossed Modules, Theory and Applications of Categories 30(25) (2015) 882-908.
  • G. J. Ellis, Higher Dimensional Crossed Modules of Algebras, Journal of Pure and Applied Algebra 52(3) (1988) 277-282.
  • A. S. -T. Lue, Non-Abelian cohomology of Associative Algebras, The Quarterly Journal of Mathematics 19(1) (1968) 159-180.
  • R. Lavendhomme, Th. Lucas, On Modules and Crossed Modules, Journal of Algebra 179 (1996) 936-963.
  • Z. Arvasi. Crossed Squares and 2-Crossed Modules of Commutative Algebras, Theory and Applications of Categories 3(7) (1997) 160-181.
  • Z. Arvasi, E. Ulualan, Homotopical Aspects of Commutative Algebras I: Freeness Conditions for Crossed Squares, Journal of Homotopy and Related Structure 10 (2013) 495-518.
  • E. S. Yılmaz, K. Yılmaz, On Crossed Squares of Commutative Algebras, Mathematical Sciences and Applications E-Notes (8) 2 (2020) 32-41.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Ummahan Ege Arslan 0000-0002-2995-0718

Serdar Hürmetli 0000-0002-7422-2138

Yayımlanma Tarihi 30 Haziran 2021
Gönderilme Tarihi 29 Mart 2021
Yayımlandığı Sayı Yıl 2021 Sayı: 35

Kaynak Göster

APA Ege Arslan, U., & Hürmetli, S. (2021). Bimultiplications and Annihilators of Crossed Modules in Associative Algebras. Journal of New Theory(35), 72-90. https://doi.org/10.53570/jnt.905298
AMA Ege Arslan U, Hürmetli S. Bimultiplications and Annihilators of Crossed Modules in Associative Algebras. JNT. Haziran 2021;(35):72-90. doi:10.53570/jnt.905298
Chicago Ege Arslan, Ummahan, ve Serdar Hürmetli. “Bimultiplications and Annihilators of Crossed Modules in Associative Algebras”. Journal of New Theory, sy. 35 (Haziran 2021): 72-90. https://doi.org/10.53570/jnt.905298.
EndNote Ege Arslan U, Hürmetli S (01 Haziran 2021) Bimultiplications and Annihilators of Crossed Modules in Associative Algebras. Journal of New Theory 35 72–90.
IEEE U. Ege Arslan ve S. Hürmetli, “Bimultiplications and Annihilators of Crossed Modules in Associative Algebras”, JNT, sy. 35, ss. 72–90, Haziran 2021, doi: 10.53570/jnt.905298.
ISNAD Ege Arslan, Ummahan - Hürmetli, Serdar. “Bimultiplications and Annihilators of Crossed Modules in Associative Algebras”. Journal of New Theory 35 (Haziran 2021), 72-90. https://doi.org/10.53570/jnt.905298.
JAMA Ege Arslan U, Hürmetli S. Bimultiplications and Annihilators of Crossed Modules in Associative Algebras. JNT. 2021;:72–90.
MLA Ege Arslan, Ummahan ve Serdar Hürmetli. “Bimultiplications and Annihilators of Crossed Modules in Associative Algebras”. Journal of New Theory, sy. 35, 2021, ss. 72-90, doi:10.53570/jnt.905298.
Vancouver Ege Arslan U, Hürmetli S. Bimultiplications and Annihilators of Crossed Modules in Associative Algebras. JNT. 2021(35):72-90.


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