Appendix:Glossary of abstract algebra
Definition from Wiktionary, the free dictionary
This is a glossary of abstract algebra
- Of an operator *, such that, for any operands a,b,c, (a * b) * c = a * (b * c).
- Of an operator *, such that, for any operands a,b, a * b = b * a.
- Of an operation * with respect to the operation o, such that a * (b o c) = (a * b) o (a * c).
- A set having two operations called addition and multiplication under both of which all the elements of the set are commutative and associative; for which multiplication distributes over addition; and for both of which there exist an identity element and an inverse element.
- A set with an associative binary operation, under which there exists an identity element, and such that each element has an inverse.
- A subring closed under multiplication by its containing ring.
- identity element
- A member of a structure which, when applied to any other element via a binary operation induces an identity mapping.
- A set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.
- An algebraic structure which is a group under addition and a monoid under multiplication.
- Any set for which there is a binary operation that is both closed and associative.
- An algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse.