Definitions for subring
sub·ring

WiktionaryRate this definition:0.0 / 0 votes

1. subringnoun

   a ring which is contained in a larger ring, such that the multiplication and addition on the former are a restriction of those on the latter

WikipediaRate this definition:0.0 / 0 votes

1. 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 R itself.

WikidataRate this definition:0.0 / 0 votes

1. 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 contains the multiplicative identity of 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. The latter gives a strictly weaker condition, even for rings that do have a multiplicative identity, so that for instance all ideals become subrings. With the initial definition, the only ideal of R that is a subring of R is R itself. A subring of a ring is a subgroup of which contains the multiplicative identity and is closed under multiplication. For example, the ring Z of integers is a subring of the field of real numbers and also a subring of the ring of polynomials Z[X]. The ring Z and its quotients Z/nZ have no subrings other than the full ring. Every ring has a unique smallest subring, isomorphic to either the integers Z or some ring Z/nZ with n a nonnegative integer.

How to pronounce subring?

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How to say subring in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of subring in Chaldean Numerology is: 4

2. Pythagorean Numerology

   The numerical value of subring in Pythagorean Numerology is: 9

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References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Subring
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Subring
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=subring