Kernel (algebra)
In the various branches of mathematics that fall under the heading of abstract algebra, the kernel of a homomorphism measures the degree to which the homomorphism fails to be injective. An important special case is the kernel of a linear map. The kernel of a matrix, also called the null space, is the kernel of the linear map defined by the matrix. In this article, we first survey kernels for some important types of algebraic structures; then we give general definitions from universal algebra for generic algebraic structures.
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Kernel (algebra)
In the various branches of mathematics that fall under the heading of abstract algebra, the kernel of a homomorphism measures the degree to which the homomorphism fails to be injective. An important special case is the kernel of a linear map. The kernel of a matrix, also called the null space, is the kernel of the linear map defined by the matrix. In this article, we first survey kernels for some important types of algebraic structures; then we give general definitions from universal algebra for generic algebraic structures.
has abstract
Der Kern einer Abbildung dient ...... Bedeutung im Homomorphiesatz.
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Em vários ramos da matemática ...... rfismo deixa de ser injectivo.
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En mathématiques et plus parti ...... amment utilisés de morphismes.
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In de lineaire algebra beeldt ...... e lineaire afbeelding genoemd.
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In matematica, in particolare ...... tano in maniera complementare.
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In the various branches of mat ...... generic algebraic structures.
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Jądro – dla danej struktury al ...... za się zwykle (od ang. kernel)
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Ядро в алгебре — характеристик ...... вают образ и фактормножество .
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في الفروع المتعددة من الرياضيا ...... خارج القسمة المعرَّف بالنواة.
@ar
在归入线性代数的各种数学分支中，同态的核测量同态不及于单射的 ...... 构定理）是应用于核所定义的商代数的采用了各种形式的一个定理。
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Der Kern einer Abbildung dient ...... Kern nur aus dem Nullvektor in
@de
Em vários ramos da matemática ...... rfismo deixa de ser injectivo.
@pt
En mathématiques et plus parti ...... e même image par le morphisme.
@fr
In de lineaire algebra beeldt ...... e lineaire afbeelding genoemd.
@nl
In matematica, in particolare ...... ati in zero dall'applicazione.
@it
In the various branches of mat ...... generic algebraic structures.
@en
Jądro – dla danej struktury al ...... za się zwykle (od ang. kernel)
@pl
Ядро в алгебре — характеристик ...... вают образ и фактормножество .
@ru
في الفروع المتعددة من الرياضيا ...... خارج القسمة المعرَّف بالنواة.
@ar
在归入线性代数的各种数学分支中，同态的核测量同态不及于单射的 ...... 构定理）是应用于核所定义的商代数的采用了各种形式的一个定理。
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label
Jądro (algebra)
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Kern (Algebra)
@de
Kern (algebra)
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Kernel (algebra)
@en
Noyau (algèbre)
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Nucleo (matematica)
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Núcleo (álgebra)
@pt
Ядро (алгебра)
@ru
نواة (جبر)
@ar
核 (代数)
@zh