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Another example is given by the natural numbers, partially ordered by divisibility, for which the supremum is the least common multiple and the infimum is the greatest common divisor. Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities.
In mathematics, many types of algebraic structures are studied. Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures may be viewed in different ways, however the common starting point of algebra texts is that an algebraic object incorporates one or more sets with one or more binary operations or unary operations satisfying a ...
In mathematics, and more specifically in order theory, several different types of ordered set have been studied. They include: Cyclic orders, orderings in which triples of elements are either clockwise or counterclockwise; Lattices, partial orders in which each pair of elements has a greatest lower bound and a least upper bound.
An algebraic structure may be based on other algebraic structures with operations and axioms involving several structures. For instance, a vector space involves a second structure called a field , and an operation called scalar multiplication between elements of the field (called scalars ), and elements of the vector space (called vectors ).
Examples are homomorphisms, which preserve algebraic structures; continuous functions, ... Its order and algebraic structure make it into an ordered field.
Pages in category "Ordered algebraic structures" The following 8 pages are in this category, out of 8 total. This list may not reflect recent changes. B.