** Noether normalization lemma

Under this formalism, angular momentum is the 2-form Noether charge associated with rotational invariance ( As a result, angular momentum is not conserved for general curved spacetimes, unless it happens to be asymptotically rotationally invariant ).

The terminology is confused, since the result is also called the Noether – Enriques theorem.

Emmy Noether showed that a slight but profound generalization of Lie's notion of symmetry can result in an even more powerful method of attack.

Noether's theorem usually refers to a result derived from work of his daughter Emmy Noether.

These conditions played an important role in the development of the structure theory of commutative rings in the works of David Hilbert, Emmy Noether, and Emil Artin.

The prime ideals of the ring of integers are the ideals ( 0 ), ( 2 ), ( 3 ), ( 5 ), ( 7 ), ( 11 ), … The fundamental theorem of arithmetic generalizes to the Lasker – Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.

The ring theory, which was firmly established during the 1920s by Emmy Noether and Wolfgang Krull, acquires a distinctly different flavor depending whether it allows rings to be commutative or not.

Though it was already incipient in Kronecker's work, the modern approach to commutative algebra using module theory is usually credited to Emmy Noether.

After his promotion, he did further studies in Göttingen under Emmy Noether, in what is now known as commutative algebra.

The name grew out of the central considerations, such as the Lasker – Noether theorem in algebraic geometry, and the ideal class group in algebraic number theory, of the commutative algebra of the first quarter of the twentieth century.

Van der Waerden credited lectures by Noether on group theory and Emil Artin on algebra, as well as a seminar conducted by Artin, Wilhelm Blaschke, Otto Schreier, and van der Waerden himself on ideals as the main references.

In mathematics, more specifically in the area of modern algebra known as ring theory, a Noetherian ring, named after Emmy Noether, is a ring in which every non-empty set of ideals has a maximal element.

The underlying drive, in Weil and Chevalley at least, was the perceived need for French mathematics to absorb the best ideas of the Göttingen school, particularly Hilbert and the modern algebra school of Emmy Noether, Artin and van der Waerden.

The influential treatment of abstract algebra by van der Waerden is said to derive in part from Artin's ideas, as well as those of Emmy Noether.

* Emmy Noether publishes Idealtheorie in Ringbereichen, developing ideal ring theory, an important text in the field of abstract algebra.

* Every automorphism of a central simple algebra is an inner automorphism ( follows from Skolem – Noether theorem ).

The Albert – Brauer – Hasse – Noether theorem establishes a local-global principle for the splitting of a central simple algebra A over an algebraic number field K. It states that if A splits over every completion K < sub > v </ sub > then it is isomorphic to a matrix algebra over K.

") probably limited the amount he learned, in particular in the " new " algebraic geometry and Artin / Noether approach to abstract algebra.

If given a label containing at least one non-ASCII character, ToASCII will apply the Nameprep algorithm, which converts the label to lowercase and performs other normalization, and will then translate the result to ASCII using Punycode before prepending the four-character string "".

Depending on the dynamic range of the content and the target level, loudness normalization can result in peaks that exceed the recording medium's limits.

A BV 1-algebra that satisfies normalization Δ ( 1 )= 0 is the same as a differential graded algebra ( DGA ) with differential Δ.

Software limitations may result in its display either in full-sized capitals ( RUN ) or in full-sized capitals of a smaller font ; either is anyway regarded as an acceptable substitute for genuine small caps .</ ref > A related concept is the lemma ( or citation form ), which is a particular form of a lexeme that is chosen by convention to represent a canonical form of a lexeme.

In mathematics, a lemma ( plural lemmata or lemmas ) from the Greek λῆμμα ( lemma, “ anything which is received, such as a gift, profit, or a bribe ”) is a proven proposition which is used as a stepping stone to a larger result rather than as a statement of interest by itself.

The diamond lemma is an important result for certain kinds of preorders.

This result is known as Schur's lemma.

In mathematics, specifically in category theory, the Yoneda lemma is an abstract result on functors of the type morphisms into a fixed object.

A related result, sometimes called the second Borel – Cantelli lemma, is a partial converse of the first Borel – Cantelli lemma.

He also proves that the Riemann – Lebesgue lemma is a best possible result for continuous functions, and gives some treatment to Lebesgue constants.

Several texts identify Tychonoff's theorem as the single most important result in general topology Willard, p. 120 ; others allow it to share this honor with Urysohn's lemma.

* Lagrange's theorem ( group theory ) or Lagrange's lemma is an important result in Group theory

In the mathematical theory of queues, Little's result, theorem, lemma, law or formula is a theorem by John Little which states:

Burnside's lemma, sometimes also called Burnside's counting theorem, the Cauchy-Frobenius lemma or the orbit-counting theorem, is a result in group theory which is often useful in taking account of symmetry when counting mathematical objects.

In more colloquial terms, in a party of people some of whom shake hands, an even number of people must have shaken an odd number of other people's hands ; for this reason, the result is known as the handshaking lemma.

* Schwarz lemma, a mathematical result about holomorphic functions

The fixed-point lemma for normal functions is a basic result in axiomatic set theory stating that any normal function has arbitrarily large fixed points ( Levy 1979: p. 117 ).

A more general form of this result is called the Pumping lemma for regular languages, which can be used to show that broad classes of languages cannot be recognized by a finite state machine.

( This result is sometimes called Berge's lemma.

A useful result pertaining to subadditive sequences is the following lemma due to Michael Fekete.

It is sometimes called Sperner's lemma, but that name also refers to another result on coloring.

In mathematics, the butterfly lemma or Zassenhaus lemma, named after Hans Julius Zassenhaus, is a technical result on the lattice of subgroups of a group or the lattice of submodules of a module, or more generally for any modular lattice.

* Schwarz's lemma, a result which in turn has many generalisations and applications in complex analysis.