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In algebra, a subring is a subobject of a ring , in i.e. the a category of rings.subobject of an object in the category Ring of rings with homomorphisms between them.

Note As with usual, there is a little bit of variation of what exactly one takes to be the nLab’s definition conventions, of if “ring” (multiplicative$A \subseteq B$unitality , then is usually understood by default, while$A$commutativity contains is usually not assumed by default) but in each case the multiplicative general unit notion of$1 \in B$subobject . reduces to the appropriare notion of subring. For instance, a subring in the category of unital rings necessarily contains theunit-element of the ambient ring, etc.

Related concepts

• subgroup, submodule

References

See also:

• Wikipedia, Subring