Associative

Right-associative operations include the following: * Exponentiation of real numbers: :: :One reason exponentiation is right-associative is that a repeated left-associative exponentiation operation would be less useful.

Addition of octonions is also associative, but multiplication of octonions is non-associative.

Associative operations are abundant in mathematics; in fact, many algebraic structures (such as semigroups and categories ) explicitly require their binary operations to be associative.

Bicategories are a weaker notion of 2-dimensional categories in which the composition of morphisms is not strictly associative, but only associative "up to" an isomorphism.

Hamilton invented the word associative so that he could say that octonions were not associative. citation Definition The octonions can be thought of as octets (or 8-tuples) of real numbers.

In this article associative algebras are assumed to have a multiplicative unit, denoted 1; they are sometimes called unital associative algebras for clarification.

Nonetheless, much of the terminology that was developed in the theory of associative rings or associative algebras is commonly applied to Lie algebras.

Still, instead of the 2-way associative scheme used in older Athlons, Thunderbird did move to a more efficient 16-way associative layout.

Since this very quality of uninhibited but largely associative speech presupposes at least a temporary lack of ego control, it may well indicate weakness rather than strength.

It is a message that bypasses the associative cortex and evokes a response from the primitive part of the brain that makes our moral decisions for us.

Actually, one can show that the subalgebra generated by any two elements of O is isomorphic to R, C, or H, all of which are associative.

A geometry constraint engine may also be employed to manage the associative relationships between geometry, such as wireframe geometry in a sketch or components in an assembly.

A group can have a non-associative pique isotope, but it cannot have a nonassociative loop isotope.

A limitation of the theory of distributions (and hyperfunctions) is that there is no associative product of two distributions extending the product of a distribution by a smooth function, as has been proved by Laurent Schwartz in the 1950s.

All of the preceding categories have the identity map as identity arrow and composition as the associative operation on arrows.

Also, caches which are not fully associative have higher chances of cache collisions even in an unfilled cache.

Associative arrays provide a mechanism for array-like functionality without huge storage overheads when the index values are sparse.

Associative combinations or cricche consist of three or four of a kind sets.

Associative deficit in recognition memory in a lifespan sample of Healthy Adults.

A substitution law holds for real power-associative algebras with unit, which basically asserts that multiplication of polynomials works as expected.