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aidb
r

ring

Algebraic structure that has compatible structures of an abelian group and a monoid, in particular having multiplicative identity

EntityQ161172

Also known as ring with identity · unital ring · associative ring · associative ring with identity · associative unital ring

Subclass of

Overview

All data

53 statements · 19% with external sources · numbers in brackets are citations

Different from
Studied by
Defining formula
  • \begin{aligned}(r+s)+t&=r+(s+t)\\r+s&=s+r\\r+0&=r\\r+(-r)&=0\\(rs)t&=r(st)\\1r=r1&=r\\r(s+t)&=rs+rt\\(r+s)t&=rt+st\end{aligned}
In defining formula
Members / parts
Underlying structure

On other databases

33 identifiers linking ring across the web's reference databases