Weighted commutators in semi-abelian categories

JOURNAL OF ALGEBRA

卷:397

Article

Gran, Marino¹  Janelidze, George²  Ursini, Aldo^3,4 

[1] Catholic Univ Louvain, Inst Rech Math & Phys, B-1348 Louvain, Belgium

[2] Univ Cape Town, Dept Math & Appl Math, ZA-7701 Cape Town, South Africa

[3] Univ Siena, Dipartimento Ingn Informaz & Sci Matemat, I-53100 Siena, Italy

[4] Univ Stellenbosch, Dept Math Sci, Div Math, ZA-7602 Matieland, South Africa

关键词: Semi-abelian categories;    Centrality;    Commutator;    Commutator terms;   

DOI  :  10.1016/j.jalgebra.2013.07.037

来源: Elsevier

【 摘 要 】

We introduce new notions of weighted centrality and weighted commutators corresponding to each other in the same way as centrality of congruences and commutators do in the Smith commutator theory. Both the Hug commutator of subobjects and Pedicchio's categorical generalization of Smith commutator are special cases of our weighted commutators; in fact we obtain them by taking the smallest and the largest weight respectively. At the end of the paper we briefly consider the universal-algebraic context in connection with an older work of the third author on the ideal theory version of the commutator theory. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free