Normalities and commutators

Giuseppe Metere, Giuseppe Metere, Sandra Mantovani

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25 Citations (Scopus)

Abstract

We first compare several algebraic notions of normality, from a categorical viewpoint. Then we introduce an intrinsic description of Higgins' commutator for ideal-determined categories, and we define a new notion of normality in terms of this commutator. Our main result is to extend to any semi-abelian category the following well-known characterization of normal subgroups: a subobject K is normal in A if. and only if, {[A, K] <= K. (C) 2010 Elsevier Inc. All rights reserved.}
Original languageEnglish
Pages (from-to)2568-2588
Number of pages21
JournalJournal of Algebra
Volume324
Publication statusPublished - 2010

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Metere, G., Metere, G., & Mantovani, S. (2010). Normalities and commutators. Journal of Algebra, 324, 2568-2588.