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.}

Mantovani, S., Metere, G. (2010). Normalities and commutators. JOURNAL OF ALGEBRA, 324(9), 2568-2588 [10.1016/j.jalgebra.2010.07.043].

Normalities and commutators

METERE, Giuseppe
2010-01-01

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.}
2010
Settore MAT/02 - Algebra
Mantovani, S., Metere, G. (2010). Normalities and commutators. JOURNAL OF ALGEBRA, 324(9), 2568-2588 [10.1016/j.jalgebra.2010.07.043].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/74837
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