Split (Pre)crossed Modules over R-Algebroids
Turkish Journal of Mathematics and Computer Science, cilt.16, sa.2, ss.411-418, 2024 (Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 16 Sayı: 2
- Basım Tarihi: 2024
- Doi Numarası: 10.47000/tjmcs.1405022
- Dergi Adı: Turkish Journal of Mathematics and Computer Science
- Derginin Tarandığı İndeksler: Scopus, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.411-418
- Anahtar Kelimeler: Algebroids, crossed modules, split epimorphisms
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Uşak Üniversitesi Adresli: Evet
Özet
In this paper, we introduce (d-)split and (d-)split+ epimorphisms and (d-)split and d-split* (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* 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.