Degree may refer to:
In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field that contains the base field and satisfies additional properties. For instance, the set Q(√2) = {a + b√2 | a, b ∈ Q} is the smallest extension of Q that includes every real solution to the equation x2 = 2.
Let L be a field. A subfield of L is a subset K of L that is closed under the field operations of L and under taking inverses in L. In other words, K is a field with respect to the field operations inherited from L. The larger field L is then said to be an extension field of K. To simplify notation and terminology, one says that L / K (read as "L over K") is a field extension to signify that L is an extension field of K.
If L is an extension of F which is in turn an extension of K, then F is said to be an intermediate field (or intermediate extension or subextension) of the field extension L / K.
The degree of an algebraic variety in mathematics is defined, for a projective variety V, by an elementary use of intersection theory.
For V embedded in a projective space Pn and defined over some algebraically closed field K, the degree d of V is the number of points of intersection of V, defined over K, with a linear subspace L in general position, when
Here dim(V) is the dimension of V, and the codimension of L will be equal to that dimension. The degree d is an extrinsic quantity, and not intrinsic as a property of V. For example the projective line has an (essentially unique) embedding of degree n in Pn.
The degree of a hypersurface F = 0 is the same as the total degree of the homogeneous polynomial F defining it (granted, in case F has repeated factors, that intersection theory is used to count intersections with multiplicity, as in Bézout's theorem).
For a more sophisticated approach, the linear system of divisors defining the embedding of V can be related to the line bundle or invertible sheaf defining the embedding by its space of sections. The tautological line bundle on Pn pulls back to V. The degree determines the first Chern class. The degree can also be computed in the cohomology ring of Pn, or Chow ring, with the class of a hyperplane intersecting the class of V an appropriate number of times.
Generic top-level domains (gTLDs) are one of the categories of top-level domains (TLDs) maintained by the Internet Assigned Numbers Authority (IANA) for use in the Domain Name System of the Internet. A top-level domain is the last label of every fully qualified domain name. They are called generic for historic reasons; initially, they were contrasted with country-specific TLDs in RFC 920.
The core group of generic top-level domains consists of the com, info, net, and org domains. In addition, the domains biz, name, and pro are also considered generic; however, these are designated as restricted, because registrations within them require proof of eligibility within the guidelines set for each.
Historically, the group of generic top-level domains included domains, created in the early development of the domain name system, that are now sponsored by designated agencies or organizations and are restricted to specific types of registrants. Thus, domains edu, gov, int, and mil are now considered sponsored top-level domains, much like the themed top-level domains (e.g., jobs). The entire group of domains that do not have a geographic or country designation (see country-code top-level domain) is still often referred to by the term generic TLDs.
Best, a compilation album by Texas-based Folk singer-songwriter Robert Earl Keen, released by Koch Records on November 7, 2006. The album features songs from six of Keen's previous albums: No Kinda Dancer, A Bigger Piece of Sky, No. 2 Live Dinner, Farm Fresh Onions, What I Really Mean, and Live at the Ryman.
The Allmusic review by Mark Deming gave the album 3½ start stating: "Robert Earl Keen is an archetypal Texas singer/songwriter, someone who can mine both laughter and tragedy from life along the dusty margins of life in the Lone Star State... a comprehensive and well-programmed compilation offering a fully rounded introduction to his music would be more than welcome. However, 2007's Best isn't quite that album... If you're looking for a concise, career-spanning overview of Robert Earl Keen's long career in music, Best isn't as much help as you might wish, but the consistent quality is a sure convincer."
All tracks by Robert Earl Keen except where noted
Best is a 2000 British film portraying the football career of the Northern Irish soccer star George Best, particularly his years spent at Manchester United. It was directed by Mary McGuckian.