Ideals and clots in universal algebra and in semi-abelian categories

JOURNAL OF ALGEBRA

卷:307

Article

Janelidze, G. ; Marki, L. ; Ursini, A.

关键词: ideals;    clots;    varieties of algebras;    semi-abelian categories;   

DOI  :  10.1016/j.jalgebra.2006.05.022

来源: Elsevier

【 摘 要 】

We clarify the relationship between basic constructions of semi-abelian category theory and the theory of ideals and clots in universal algebra. To name a few results in this frame, which establish connections between hitherto separated subjects, 0-regularity in universal algebra corresponds to the requirement that regular epimorphisms are normal; we describe clots in categorical terms and show that ideals are images of clots under regular epimorphisms; we show that the relationship between internal precrossed modules and internal reflexive graphs extends the relationship between compatible reflexive binary relations and clots. (C) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free