Bimultipliers of R-algebroids

Yıl 2024, Cilt: 6 Sayı: 1, 30 - 40

Gizem Kahrıman

https://doi.org/10.54286/ikjm.1433913

Öz

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.

Anahtar Kelimeler

R-algebroid, Bimultiplier, Multiplication

Kaynakça

• S.Mac Lane, Extensions and Obstructures for Rings, Illinois J.Math., 121 , (1958), 316-345.
• Z. Arvasi, U. Ege, Anihilators, Multipliers and Crossed Modules, Applied Categorical Structures, (2003), 11:487-506.
• B.Mitchell, Rings with several objects, Advances inMathematics, 8(1), (1972), 1-161.
• B.Mitchell, Some applications of module theory to functor categories, Bull. Amer.Math. Soc., (1978), 84, 867-885.
• B.Mitchell, Separable algebroids,Mem. Amer.Math. Soc., (1985), 57, 333, 96 pp.
• S.M. Amgott, Separable categories, Journal of Pure and Applied Algebra, (1986), 40, 1-14.
• G.H. Mosa, Higher dimensional algebroids and crossed complexes, PhD Thesis, University College of NorthWales, Bangor, (1986).
• O. Avcıoglu, I.I. Akça, Coproduct of Crossed A-Modules of R-algebroids, Topological Algebra and its Applications, (2017), 5, 37-48.
• O. Avcıoglu, I.I. Akça, Free modules and crossed modules of R-algebroids, Turkish Journal of Mathematics, (2018), 42: 2863-2875.
• O. Avcıoglu, I.I. Akça, On generators of Peiffer ideal of a pre-R-algebroid in a precrossed module and applications, NTMSCI 5, No. 4, (2017), 148-155.
• O. Avcıoglu, I.I. Akça, On Pullback and Induced Crossed Modules of R-Algebroids, Commun. Fac.Sci.Univ.Ank.Series A1, Vol 66, 2, (2017), 225-242.
• I.I. Akca, O. Avcıoglu, Equivalence between (pre) cat 1-R-algebroids and (pre) crossed modules of Ralgebroids, Bull.Math. Soc. Sci.Math. Roumanie Teme (110) No-3, (2022), 267-288.
• U. Ege Arslan, S. Hurmetli, Bimultiplications and Annihilators of CrossedModules in Associative Algebras, Journal of New Theory, 2021.
• U. Ege Arslan, On the Actions of Associative Algebras, Innovative Research in Natural Science and Mathematics, ISBN:978-625-6507-13-5, 1-15.
• J. Doncel, A. Grandje´an, M. Vale, On the homology of commutative algebras. Journal of Pure and Applied Algebra, (1992), 79(2):131–157.
• A. Grandje´an, M. Vale, 2-m´odulos cruzados en la cohomolog´ıa de Andr´e-Quillen. Real Academia de Ciencias Exactas, F´ısicas y Naturales deMadrid, 1986.
• I.I. Akca , K. Emir, J.F.Martins, Pointed homotopy of 2-crossed module maps of commutative algebras, Homology Homotopy Appl. 18(1):99–128, 2016.
• I.I. Akça, K. Emir, J.F.Martins, Two-fold homotopy of 2-crossed module maps of commutative algebras. Commun. Algebra 47(1), (2019), 289–311
• I.I. Akça, O. Avcıoglu, Homotopies of crossed complex morphisms of associative R-algebras. Georgian Math. J. 28(2), (2021), 163–172.
• U.E. Arslan, I.I. Akca, G.O. Irmak, O. Avcıoglu, Fibrations of 2-crossed modules.MathematicalMethods in the Applied Sciences, (2018), 42(16), 5293-5304.
• I.I. Akça, S. Pak, Pseudo simplicial groups and crossed modules, Turk J.Math., 34, (2010), 475-487.