Associator

In abstract algebra, the term associator is used in different ways as a measure of the nonassociativity of an algebraic structure.

Ring theory

For a nonassociative ring or algebra , the associator is the multilinear map given by

Just as the commutator measures the degree of noncommutativity, the associator measures the degree of nonassociativity of . It is identically zero for an associative ring or algebra.

The associator in any ring obeys the identity

The associator is alternating precisely when is an alternative ring.

The associator is symmetric in its two rightmost arguments when is a pre-Lie algebra.

The nucleus is the set of elements that associate with all others: that is, the n in R such that

It turns out that any two of being implies that the third is also the zero set.

Quasigroup theory

A quasigroup Q is a set with a binary operation such that for each a,b in Q, the equations and have unique solutions x,y in Q. In a quasigroup Q, the associator is the map defined by the equation

Nucleus (advocacy group)

Nucleus was a British-European advocacy group, the forerunner to British Influence (sometimes The Centre for British Influence). Nucleus was based in London, with additional operations in Brussels.

Founded in 2010, Nucleus promoted a 'euro-realist' British approach to European political and business affairs. As well as regular bulletins, Nucleus produced commentaries, and hosted briefings, seminars, and networking events both in London and Brussels. Nucleus was unaffiliated with any political party, and was a partner in both the British Brussels Network, along with Business for New Europe, the British Chamber of Commerce in Belgium, and the Institute of Chartered Accountants in England and Wales, and the pan-European EuropAssociation.

In 2013 Nucleus relaunched as British Influence, with a heavier campaigning focus, in response to the call by Prime Minister David Cameron for an in/out referendum on the UK's European Union membership

References

External links

Nucleus (order theory)

In mathematics, and especially in order theory, a nucleus is a function on a meet-semilattice such that (for every in ):

Every nucleus is evidently a monotone function.

Frames and locales

Usually, the term nucleus is used in frames and locales theory (when the semilattice is a frame).

Proposition: If is a nucleus on a frame , then the poset of fixed points of , with order inherited from , is also a frame.

References

Space

Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.

Space (The Arrogant Worms album)

Space, stylized as SPACE, is the fourteenth album by the Canadian comedy music group, The Arrogant Worms. It was released in March 2014.

Track listing

Space (novel)

Space is a novel by James A. Michener published in 1982. It is a fictionalized history of the United States space program, with a particular emphasis on manned spaceflight.

Michener writes in a semi-documentary style. The topics explored in the novel include naval warfare in the Pacific, air combat in the Korean War (something Michener had already explored in The Bridges at Toko-Ri), test pilot life at 'Pax River', astronaut selection and training, the role of the media in promoting the space program as a national achievement, and the development of the Gemini and Apollo spacecraft, the rise of the military-industrial complex and the evolution of NACA into NASA.

Plot summary

The story begins in 1944 and covers more than 30 years in the lives of four men and their families: Dieter Kolff, a German rocket scientist who worked for the Nazis; Norman Grant, a World War II hero turned U.S. Senator from a fictional mid-west state; Stanley Mott, an aeronautical engineer charged with a top-secret U.S. government mission to rescue Kolff from Peenemünde; and John Pope, a small-town boy turned Naval Aviator who becomes a test pilot and then an astronaut. Randy Claggett, a rambunctious Marine Corps aviator and astronaut, is considered by Michener to be the most important supporting character (the first two parts of the book are entitled "Four Men" and "Four Women"). The lives of the fictional characters interweave with those of historical figures, such as Wernher von Braun and Lyndon Johnson. A group of trainee astronauts are introduced to fly fictional but plausible Project Gemini and Project Apollo missions; the intensive training and jockeying for position amongst the astronauts forms much of the background of the middle of the novel, reminiscent of a fictional version of Tom Wolfe's The Right Stuff and the movie as well.