* Any ring of characteristic n is a ( Z / nZ )- algebra in the same way.

* Any ring A is an algebra over its center Z ( A ), or over any subring of its center.

* Any two objects Y and Z of C have an exponential Z < sup > Y </ sup > in C.

:: Theorem ( Lefschetz theorem on ( 1, 1 )- classes ) Any element of H < sup > 2 </ sup >( X, Z ) ∩ H < sup > 1, 1 </ sup >( X ) is the cohomology class of a divisor on X.

Any simplicial automorphism φ of X defines a permutation π of Z / n Z such that label ( φ ( M ))

Any scheme S has a unique morphism to Spec ( Z ), so this attitude, part of the relative point of view, doesn't lose anything.

* Any ring of p-adic integers Z < sub > p </ sup > for a given prime p is a local ring, with field of fractions the p-adic numbers Q < sub > p </ sub >.

Any prime p ≡ 1 mod 4 splits into two distinct prime ideals in Z ; this is a manifestation of Fermat's theorem on sums of two squares.

#" By Any Other Way ” Music: S. Björnshög Lyrics: Z. Gram

* Any commutative ring R is an algebra over itself, or any subring of R.

Any Banach algebra ( whether it has an identity element or not ) can be embedded isometrically into a unital Banach algebra so as to form a closed ideal of.

Any field may be used as the scalars for a vector space, which is the standard general context for linear algebra.

* Any vector space V endowed with the identically zero Lie bracket becomes a Lie algebra.

Any one-dimensional Lie algebra over a field is abelian, by the antisymmetry of the Lie bracket.

* Any Lie group G defines an associated real Lie algebra.

Any algebra whose elements are idempotent is also power-associative.

:“ Any linear map from V to an algebra A can be uniquely extended to an algebra homomorphism from T ( V ) to A .”

A weight on a Lie algebra g over a field F is a linear map λ: g → F with λ ( y )= 0 for all x, y in g. Any weight on a Lie algebra g vanishes on the derived algebra and hence descends to a weight on the abelian Lie algebra g /.

Any associative algebra A over the field K becomes a Lie algebra over K with the Lie bracket:

: Any linear transformation f: V → A from V to an algebra A over K can be uniquely extended to an algebra homomorphism from T ( V ) to A as indicated by the following commutative diagram:

* Any algebra over a commutative ring K may be regarded as a purely even superalgebra over K ; that is, by taking A < sub > 1 </ sub > to be trivial.

Any n-dimensional formal group law gives an n dimensional Lie algebra over the ring R, defined in terms of the quadratic part F < sub > 2 </ sub > of the formal group law.

Any affine group scheme is the spectrum of a commutative Hopf algebra ( over a base S, this is given by the relative spectrum of an O < sub > S </ sub >- algebra ).

Any abilities I may have were achieved in their present shape from experience in sharing in the growth and control of my business, coupled with raising my family.

Any claimant whose claim is denied, or is approved for less than the full amount of such claim, shall be entitled, under such regulations as the Commission may prescribe, to a hearing before the Commission, or its duly authorized representatives, with respect to such claim.

Any example of grand or exquisite diction may have been created by the poet who compiled numerous lays into the two works we possess or may be due to one of his completely unknown fellow-craftsmen.

Any flat-bed press capable of pressing a specimen 22 inches square may be used as an alternative.

Any place called Altenberg may have given rise to Altenberg as a family name, such as:

Any information may be conveyed by an analog signal ; often such a signal is a measured response to changes in physical phenomena, such as sound, light, temperature, position, or pressure.

Any player may declare the game over at any time during his turn if either of two conditions is true: one chain has 41 or more tiles, or there is at least one chain on the board and every chain on the board has 11 or more tiles.

Any number of players may be replaced by substitutes during the course of the game.

Any of these may be sources of essential amino acids.

Any of these reactions may be used in LPCVD, but the silane reaction is also done in APCVD.

Any player may block another player's passage, so long as he does not hold or trip the player he intends to block.

Any large, smoothbore, muzzle-loading gun — used before the advent of breech-loading, rifled guns — may be referred to as a cannon, though once standardized names were assigned to different sized cannons, the term specifically referred to a gun designed to fire a shot, as opposed to a demi-cannon-, culverin-, or demi-culverin-.

Any string of characters may or may not be a well-formed name for a file or a link depending upon the context of application.

# Any experience which is inconsistent with the organization of the structure of the self may be perceived as a threat, and the more of these perceptions there are, the more rigidly the self structure is organized to maintain itself.

Any suggestion I may have made to you will be without force when I say the word ' cancelled.

Any rational number with a denominator whose only prime factors are 2 and / or 5 may be precisely expressed as a decimal fraction and has a finite decimal expansion.

* Any scalar or other field may have a dipole moment.

Any elected or appointed board, committee, town officer or ten voters, may place an article on the warrant.

Any form of energy may be transformed into another form.

Any consistent set of units may be used, although SI units are preferred.

Any voluntary muscle in the body may be affected, although the tremor is most commonly seen in the hands and arms and slightly less commonly in the neck ( causing the patient's head to shake ), tongue, and legs.

Any minister and the cabinet as a whole however must have continuing trust of the parliament and may be voted out, resign or be replaced.