## Quick Reference

*R* on which there are defined two dyadic operations, normally denoted by + (addition) and · or juxtaposition (multiplication). With respect to addition, *R* is an abelian group,〈*R*, +〉i.e. + is commutative and associative. With respect to multiplication, *R* is a semigroup,〈*R*, ·〉i.e. · is associative. Further, multiplication is distributive over addition.

〈*R*, +〉

〈*R*, ·〉

Certain kinds of rings are of particular interest:*R*, ·〉 is a monoid, the ring is called a ring with an identity;*x* and *y* with the property that *x* · *y* = 0, is said to be an **integral domain**;

*R*, ·〉 is a monoid, the ring is called a ring with an identity;

*x* and *y* with the property that *x* · *y* = 0, is said to be an **integral domain**;

The concept of a ring provides an algebraic structure into which can be fitted such diverse items as the integers, polynomials with integer coefficients, and matrices; on all these items it is customary to define two dyadic operations.

*Another name for* circular list, but more generally applied to any list structure where all sublists as well as the list itself are circularly linked.

**From:**
ring
in
A Dictionary of Computing »

*Subjects:*
Computing.

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