Normalities and commutators

Giuseppe Metere, Giuseppe Metere, Sandra Mantovani

Risultato della ricerca: Article

23 Citazioni (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.}
Lingua originaleEnglish
pagine (da-a)2568-2588
Numero di pagine21
RivistaDefault journal
Volume324
Stato di pubblicazionePublished - 2010

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Commutator
Normality
Semi-abelian Category
Normal subgroup
Categorical

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cita questo

Metere, G., Metere, G., & Mantovani, S. (2010). Normalities and commutators. Default journal, 324, 2568-2588.

Normalities and commutators. / Metere, Giuseppe; Metere, Giuseppe; Mantovani, Sandra.

In: Default journal, Vol. 324, 2010, pag. 2568-2588.

Risultato della ricerca: Article

Metere, G, Metere, G & Mantovani, S 2010, 'Normalities and commutators', Default journal, vol. 324, pagg. 2568-2588.
Metere G, Metere G, Mantovani S. Normalities and commutators. Default journal. 2010;324:2568-2588.
Metere, Giuseppe ; Metere, Giuseppe ; Mantovani, Sandra. / Normalities and commutators. In: Default journal. 2010 ; Vol. 324. pagg. 2568-2588.
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AU - Metere, Giuseppe

AU - Mantovani, Sandra

PY - 2010

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AB - 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.}

KW - Commutator

KW - Ideal

KW - Normal subobject

KW - Semi-abelian

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