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 i...
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http://en.wikipedia.org/wiki/Subring
a subset of a ring that is a subgroup under addition and that is closed under multiplication. Cf. (def. 22).
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https://www.infoplease.com/dictionary/subring
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