Frame

. Again under mild hypotheses of finiteness, this function is a polynomial, the Hilbert polynomial, for all large enough values of n (see also Hilbert-Samuel polynomial). The Frames is also the name of an Irish rock band, fronted by Glen Hansard. This idea is much used in commutative algebra, and elsewhere, to define under mild hypotheses a Hilbert function, namely the length of M_n as a function of n. The word also has many extended, metaphorical meanings in various fields:. and. It is used in this basic sense in art, construction, and mechanical engineering, and the expression 'frame' for eyeglasses. The corresponding idea in module theory is that of a graded module, namely a module M over A such that also.

A frame or framework is a structural system or a skeleton that supports other components of the object. Category theoretically, a G-graded algebra A is an object in the category of G-graded vector spaces together with a morphism of the degree of the identity of G. one complete game of snooker; a match usually comprises at least three frames. Examples of G-graded algebras include:. in psychology, Framing (psychology). (If we don't require that the ring has an identity element, we can extend the definition from monoids to semigroups. in law, to frame someone is to make it look as if they committed a crime when they in fact did not commit said crime, as in the title of the movie Who Framed Roger Rabbit; see frameup. A graded algebra is then the same thing as a N-graded algebra, where N is the monoid of natural numbers.

See frame (dance). such that. the connection between lead and follow in partner dancing. A G-graded algebra A is an algebra with a direct sum decomposition. each player's turn in bowling games. We can generalize the definition of a graded algebra to an arbitrary monoid G as an index set. also in mathematics, a frame can refer to a complete Heyting algebra. One example is the close relationship between homogeneous polynomials and projective varieties.

Also projective frame. Graded algebras are much used in commutative algebra and algebraic geometry, homological algebra and algebraic topology. See vierbein for an orthonormal frame. Examples of graded algebras are common in mathematics:. in mathematics, a frame is an abstract concept on a manifold, generalising frame of reference to a basis for the tangent bundle varying from point to point. Since rings may be regarded as Z-algebras, a graded ring is defined to be a graded Z-algebra. a frame of reference in physics. An ideal, or other set in A, is homogeneous if for every element a it contains, the homogeneous parts of a are also contained in it.

a narrative frame in literature, film, or storytelling. Elements of A_n are known as homogeneous elements of degree n. a frame tale in literature. such that. Semantic frames in cognitive science, linguistics, or communication theory. A graded algebra A is an algebra that has a direct sum decomposition. the frame problem in artificial intelligence, a data structure for representing a stereotyped situation. .

the frame element in HTML; see HTML element#Frames. In mathematics, in particular abstract algebra, a graded algebra is an algebra over a field (or commutative ring) with an extra piece of structure, known as a grading. in computer science, a stack frame. Here the homogeneous elements are either even (degree 0) or odd (degree 1). in telecommunications, a data frame is a transmitted packet. Clifford algebras are a common family of examples. reframing in film and programming. A superalgebra is another term for a Z₂-graded algebra.

in video compression different frames –- called I-frames, P-frames, B-frames, and D-frames –- are used for motion compensation. The group ring of a group is naturally graded by that group; similarly, monoid rings are graded by the corresponding monoid. a complete image, or the set of all picture elements representing it, in video display. The cohomology ring H^• in any cohomology theory is also graded, being the direct sum of the Hⁿ. one of the film frames or video frames composing a film or video