Araştırma Makalesi
Yıl 2023,
Cilt: 52 Sayı: 3, 698 - 707, 30.05.2023
Öz
Kaynakça
- [1] R. Brown and O. Mucuk, Covering groups of non-connected topological groups revis- ited, Math. Proc. Camb. Philos. Soc. 115, 97–110, 1994.
- [2] R. Brown and C. B. Spencer, G-groupoids, crossed modules and the fundamental groupoid of a topological group, Indag. Math. (N.S.) 79, 296–302, 1976.
- [3] G. J. Ellis, Higher dimensional crossed modules of algebras, J. Pure Appl. Algebra, 52 (3), 277–282, 1988.
- [4] B. Mitchell, Rings with several objects, Advances in Mathematics, 8 (1) 1–161, 1972.
- [5] B. Mitchell, Some applications of module theory to functor categories, Bull. Amer. Math. Soc. 84, 867–885, 1978.
- [6] B. Mitchell, Separable Algebroids, Mem. Amer. Math. Soc. 57 (333), 96 pp, 1985.
- [7] G. H. Mosa, Higher dimensional algebroids and crossed complexes, PhD Thesis, University College of NorthWales, Bangor, 1986.
- [8] O. Mucuk, T. Şahan and N. Alemdar, Normality and Quotients in Crossed Modules and Group-groupoids. Appl. Categ. Structures 23 (3), 415–428, 2015.
- [9] K. Norrie, Actions and automorphisms of crossed modules, Bull. Soc. Math. France, 118 (2), 129–146, 1990.
- [10] T. Porter, Homology of commutative algebras and an invariant of Simis and Vascon- celos, J. Algebra, 99, 458–465, 1986.
- [11] T. Porter, Extensions, crossed modules and internal categories in categories of groups with operations, Proc. Edinb. Math. Soc. 30, 373–381, 1987.
- [12] N. M. Shammu, Algebraic and categorical structure of categories of crossed modules of algebras, PhD Thesis, University College of North Wales, Bangor, 1992.
- [13] T. Şahan and O. Mucuk, Normality and Quotient in the Category of Crossed Modules Within the Category of Groups with Operations, Bol. Soc. Paran. Mat. 38 (7), 169– 179, 2020.
Yıl 2023,
Cilt: 52 Sayı: 3, 698 - 707, 30.05.2023
Öz
In this paper, using the equivalence between the category of crossed modules of algebras and the category of algebra-algebroids, we will explore the notions of ideality and factors for these algebraic structures. We give the structure of a two sided ideal of an algebra-algebroid and the notion of quotient algebra-algebroid. By considering a two sided ideal of an algebra-algebroid, we show that the crossed module corresponding to this ideal is a crossed ideal of the crossed module corresponding to the algebra-algebroid. Conversely, by taking a crossed ideal of a crossed module, we also show that the corresponding algebra-algebroid to this crossed ideal is an ideal of the algebra-algebroid corresponding to the crossed module.
Anahtar Kelimeler
Kaynakça
- [1] R. Brown and O. Mucuk, Covering groups of non-connected topological groups revis- ited, Math. Proc. Camb. Philos. Soc. 115, 97–110, 1994.
- [2] R. Brown and C. B. Spencer, G-groupoids, crossed modules and the fundamental groupoid of a topological group, Indag. Math. (N.S.) 79, 296–302, 1976.
- [3] G. J. Ellis, Higher dimensional crossed modules of algebras, J. Pure Appl. Algebra, 52 (3), 277–282, 1988.
- [4] B. Mitchell, Rings with several objects, Advances in Mathematics, 8 (1) 1–161, 1972.
- [5] B. Mitchell, Some applications of module theory to functor categories, Bull. Amer. Math. Soc. 84, 867–885, 1978.
- [6] B. Mitchell, Separable Algebroids, Mem. Amer. Math. Soc. 57 (333), 96 pp, 1985.
- [7] G. H. Mosa, Higher dimensional algebroids and crossed complexes, PhD Thesis, University College of NorthWales, Bangor, 1986.
- [8] O. Mucuk, T. Şahan and N. Alemdar, Normality and Quotients in Crossed Modules and Group-groupoids. Appl. Categ. Structures 23 (3), 415–428, 2015.
- [9] K. Norrie, Actions and automorphisms of crossed modules, Bull. Soc. Math. France, 118 (2), 129–146, 1990.
- [10] T. Porter, Homology of commutative algebras and an invariant of Simis and Vascon- celos, J. Algebra, 99, 458–465, 1986.
- [11] T. Porter, Extensions, crossed modules and internal categories in categories of groups with operations, Proc. Edinb. Math. Soc. 30, 373–381, 1987.
- [12] N. M. Shammu, Algebraic and categorical structure of categories of crossed modules of algebras, PhD Thesis, University College of North Wales, Bangor, 1992.
- [13] T. Şahan and O. Mucuk, Normality and Quotient in the Category of Crossed Modules Within the Category of Groups with Operations, Bol. Soc. Paran. Mat. 38 (7), 169– 179, 2020.
Toplam 13 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Mayıs 2023 |
| Yayımlandığı Sayı | Yıl 2023 Cilt: 52 Sayı: 3 |