TY  - JOUR
T1  - Split (Pre)crossed Modules over $R$-Algebroids
AU  - Avcıoğlu, Osman
PY  - 2024
DA  - December
Y2  - 2024
DO  - 10.47000/tjmcs.1405022
JF  - Turkish Journal of Mathematics and Computer Science
JO  - TJMCS
PB  - Matematikçiler Derneği
WT  - DergiPark
SN  - 2148-1830
SP  - 411
EP  - 418
VL  - 16
IS  - 2
LA  - en
AB  - 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.
KW  - Algebroids
KW  - crossed modules
KW  - split epimorphisms.
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UR  - https://doi.org/10.47000/tjmcs.1405022
L1  - https://dergipark.org.tr/en/download/article-file/3600194
ER  -