Ring extension

Adjunction of a ring

Let be a subring and be an arbitrary set of elements. The ring of adjoin is the ring generated by , i.e. the smallest possible subring of containing . #m/def/ring

• If is an integral domain, then its field of fractions is denoted .
• The same notation can be used for adjoining a single element, e.g. or .
• If the ambient ring is left unspecified and is a monoid, one considers the Monoid ring.
• See also polynomial ring
• Category ring

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