Ringlike Structures
The following structures include generalizations and other algebraic objects similar to rings.
- Nearring
- A structure that is a group under addition, a semigroup under multiplication, and whose multiplication distributes on the right over addition.
- Rng
- An algebraic structure satisfying the same properties as a ring, except that multiplication need not have an identity element. The term "rng" is meant to suggest that it is a "ring" without an "identity".
- Semiring
- An algebraic structure satisfying the same properties as a ring, except that addition need only be an abelian monoid operation, rather than an abelian group operation. That is, elements in a semiring need not have additive inverses.
Read more about this topic: Glossary Of Ring Theory
Famous quotes containing the word structures:
“The philosopher believes that the value of his philosophy lies in its totality, in its structure: posterity discovers it in the stones with which he built and with which other structures are subsequently built that are frequently better—and so, in the fact that that structure can be demolished and yet still possess value as material.”
—Friedrich Nietzsche (1844–1900)