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Any and commutative

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

* Any ring of matrices with coefficients in a commutative ring R forms an R-algebra under matrix addition and multiplication.

Any commutative monoid is endowed with its algebraic preordering ≤, defined by x ≤ y if and only if there exists z such that x + z = y.

Any number system that forms a commutative ring — for instance, the integers, the real numbers, and the complex numbers — can be extended to a wheel in which division by zero is always possible ; however, in such a case, " division " has a slightly different meaning.

* Any commutative ring becomes a *- ring with the trivial involution.

: 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 bounded, distributive lattice is a commutative, idempotent semiring under join and meet.

* 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 module over a commutative ring R is automatically a bimodule.

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 complete group variety ( variety here meaning reduced and geometrically irreducible separated scheme of finite type over a field ) is automatically commutative, by an argument involving the action of conjugation on jet spaces of the identity.

Any commutative algebra is a supercommutative algebra if given the trivial gradation ( i. e. all elements are even ).

Any and semigroup

Any associative magma ( semigroup ) is clearly alternative.

Any transformation semigroup can be turned into a semigroup action by the following construction.

Any free inverse semigroup is F-inverse.

Any and is

Any organism that falters or misperceives the signals or weakens is done.

Any information we have here in Taiwan is at your disposal ''.

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 alteration of one of these factors is distortion, although we generally use that word only for effects so pronounced that they can be stated quantitatively on the basis of standard tests.

Any musician playing Beethoven here, where Beethoven was born, is likely to examine his own interpretations with special care.

Any action is understood to create " seeds " in the mind that sprout into the appropriate results ( Pāli vipaka ) when they meet the right conditions.

** Any union of countably many countable sets is itself countable.

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 quantity of energy absorbed by the electron in excess of this amount is converted to kinetic energy according to the conservation of energy.

Any breach of these laws is a criminal offence and can lead to fine of up to £ 5, 000 or six months in prison.

The prohibition against retaliation or coercion applies broadly to any individual or entity that seeks to prevent an individual from exercising his or her rights or to retaliate against him or her for having exercised those rights ... Any form of retaliation or coercion, including threats, intimidation, or interference, is prohibited if it is intended to interfere.

Any word or phrase that exactly reproduces the letters in another order is an anagram.

Any work ( δW ) done must be done at the expense of internal energy U, since no heat δQ is being supplied from the surroundings.

" Any threat of war Clovis could make would only be effective if they were neighbors ; " it is nowhere written that Syagrius was handed over in 486 or 487.

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 person who is seen as a threat to civil aviation is banned from flying.

* 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 form of intelligent life would do ; so, specifying carbon-based life, per se, is irrelevant.

* Any base that is water-soluble and forms hydroxide ions or the solution of a base in water.

Any and medial

Any definite conclusion to Cynewulf being either Northumbrian or Mercian has been hard to come by, but linguistic evidence suggests that the medial e in the signed Cynewulf would have, during the broad window period of Cynewulf ’ s existence, been characteristic of a Mercian dialect.

Any and magma

Any subsequent eruption may produce distinctly layered deposits, for example the deposits from the 79 AD eruption of Mount Vesuvius include a thick layer of white pumice from the upper portion of the magma chamber overlayed with a similar layer of grey pumice produced from material erupted later from lower down in the chamber.

Any of the three main types of rocks ( igneous, sedimentary, and metamorphic rocks ) can melt into magma and cool into igneous rocks.

Any and has

Any tragedy, he maintains, has six elements: plot, character, and thought ( the objects of imitation ), diction and melody ( the means of imitation ), and spectacle ( the manner of imitation ).

Any street meeting, sacred or secular, which he and his colleagues uneasily cover has as its explicit or implicit burden the cruelty and injustice of the white domination.

Any string s has at least one description, namely the program:

Any individual has one of six possible genotypes ( AA, AO, BB, BO, AB, and OO ) that produce one of four possible phenotypes: " A " ( produced by AA homozygous and AO heterozygous genotypes ), " B " ( produced by BB homozygous and BO heterozygous genotypes ), " AB " heterozygotes, and " O " homozygotes.

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 collection of closed subsets of X with the finite intersection property has nonempty intersection.

Any young player who has good control will become a successful curve pitcher long before the pitcher who is endeavoring to master both curves and control at the same time.

Any use of the term " Cathar " to refer to people after the suppression of Catharism in the 14th century is a cultural or ancestral reference, and has no religious implication.

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 configuration of charges or currents has a ' dipole moment ', which describes the dipole whose field is the best approximation, at large distances, to that of the given configuration.

Any such poset has a dual poset.

:* Any total order on X has exactly one equivalence class, X itself, because x ~ y for all x and y ;

:* Any subset of the identity relation on X has equivalence classes that are the singletons of X.

# Disturbed natural forest – Any forest type above that has in its interior significant areas of disturbance by people, including clearing, felling for wood extraction, anthropogenic fires, road construction, etc.

Any symbolism has been added later to the three colours, although the orange comes from the House of Orange-Nassau.

Any normal subgroup has a corresponding quotient group, formed from the larger group by eliminating the distinction between elements of the subgroup.

For instance, the Archbishop of Wales has criticized " atheistic fundamentalism " broadly and said " Any kind of fundamentalism, be it Biblical, atheistic or Islamic, is dangerous ".

Any attempt to define it ( X is good if it has property Y ) will simply shift the problem ( Why is Y-ness good in the first place?

Any right action has an equivalent left action, thus only left actions can be considered without any loss of generality.

Any one language has only a subset of the aspectual distinctions attested in the world's languages, and some languages ( such as Standard German ; see below ) do not have aspects.

In an inertial frame, Newton's first law ( the law of inertia ) is satisfied: Any free motion has a constant magnitude and direction.

Any conductor has inductance.

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