Subring
In mathematics, a subring of R is a subset of a ring that is itself a ring when binary operations of addition and multiplication on R are restricted to the subset, and which shares the same multiplicative identity as R. For those who define rings without requiring the existence of a multiplicative identity, a subring of R is just a subset of R that is a ring for the operations of R (this does imply it contains the additive identity of R). The latter gives a strictly weaker condition, even for rings that do have a multiplicative identity, so that for instance all ideals become subrings (and they may have a multiplicative identity that differs from the one of R). With definition requiring a multiplicative identity (which is used in this article), the only ideal of R that is a subring of R is
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Subring
In mathematics, a subring of R is a subset of a ring that is itself a ring when binary operations of addition and multiplication on R are restricted to the subset, and which shares the same multiplicative identity as R. For those who define rings without requiring the existence of a multiplicative identity, a subring of R is just a subset of R that is a ring for the operations of R (this does imply it contains the additive identity of R). The latter gives a strictly weaker condition, even for rings that do have a multiplicative identity, so that for instance all ideals become subrings (and they may have a multiplicative identity that differs from the one of R). With definition requiring a multiplicative identity (which is used in this article), the only ideal of R that is a subring of R is
has abstract
Dalam matematika, subgelanggan ...... g dari R adalah R itu sendiri.
@in
En mathématiques, un sous-anne ...... me neutre multiplicatif que A.
@fr
In de ringtheorie, een deelgeb ...... tiplicatieve identiteit heeft.
@nl
In mathematics, a subring of R ...... is a subring of R is R itself.
@en
Podpierścień – podzbiór pierśc ...... ny jest brak dzielników zera).
@pl
Подкольцо кольца — это пара , ...... одкольцом кольца многочленов .
@ru
Підкільце кільця — це пара , д ...... ідкільцем кільця многочленів .
@uk
数学における部分環(ぶぶんかん、英: subring)は、環 ...... 合には、R の部分環となるようなイデアルは R 自身に限る。
@ja
設(R,+,·)為环,若S是R的一個非空子集,且(S,+,·)也是環,則稱(S,+,·)為(R,+,·)的子環(subring)。
@zh
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Dalam matematika, subgelanggan ...... multiplikatif (yang digunakan
@in
En mathématiques, un sous-anne ...... me neutre multiplicatif que A.
@fr
In de ringtheorie, een deelgeb ...... dat idealen deelringen worden.
@nl
In mathematics, a subring of R ...... of R that is a subring of R is
@en
Podpierścień – podzbiór pierśc ...... ny jest brak dzielników zera).
@pl
Подкольцо кольца — это пара , ...... горным взглядом на математику.
@ru
Підкільце кільця — це пара , д ...... рійним поглядом на математику.
@uk
数学における部分環(ぶぶんかん、英: subring)は、環 ...... 合には、R の部分環となるようなイデアルは R 自身に限る。
@ja
設(R,+,·)為环,若S是R的一個非空子集,且(S,+,·)也是環,則稱(S,+,·)為(R,+,·)的子環(subring)。
@zh
label
Deelring
@nl
Podpierścień
@pl
Sous-anneau
@fr
Subgelanggang
@in
Subring
@en
Подкольцо
@ru
Підкільце
@uk
子環
@zh
部分環
@ja
부분환
@ko