Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9497251 | Journal of Pure and Applied Algebra | 2005 | 14 Pages |
Abstract
Given a regular epimorphism
f:Xâ Y in an exact homological category
C, and a pair
(U,V) of kernel subobjects of X, we show that the quotient
(f(U)â©f(V))/f(Uâ©V) is always abelian. When
C is nonpointed, i.e. only exact protomodular, the translation of the previous result is that, given any pair
(R,S) of equivalence relations on X, the difference mappingδ:Y/f(Râ©S)â Y/(f(R)â©f(S)) has an abelian kernel relation. This last result actually holds true in any exact Mal'cev category. Setting
Y=X/T, this result says that the difference mapping determined by the inclusion
Tâª(Râ©S)⩽(TâªR)â©(TâªS) has an abelian kernel relation, which casts a new light on the congruence distributive property.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Dominique Bourn,