near-ring
Sign in to saveIn mathematics, a near-ring (also near ring or nearring) is an algebraic structure similar to a ring but satisfying fewer axioms. Near-rings arise naturally from functions on groups.
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6 sectionsContents
- Definition
- Mappings from a group to itself
- Applications
- See also
- References
- External links
In mathematics, a near-ring (also near ring or nearring) is an algebraic structure similar to a ring but satisfying fewer axioms. Near-rings arise naturally from functions on groups.
== Definition == A set N together with two binary operations + (called addition) and ⋅ (called multiplication) is called a (right) near-ring if: N is a group (not necessarily abelian) under addition; multiplication is associative (so N is a semigroup under multiplication); and multiplication on the right distributes over addition: for any x, y, z in N, it holds that (x + y)⋅z = (x⋅z) + (y⋅z).