Every associative algebra is obviously alternative, but so too are some strictly nonassociative algebras such as the octonions.

Every associative algebra is obviously power-associative, but so are all other alternative algebras ( like the octonions, which are non-associative ) and even some non-alternative algebras like the sedenions.

* Every polynomial ring R ..., x < sub > n </ sub > is a commutative R-algebra.

Every ridge arises as the intersection of two facets ( but the intersection of two facets need not be a ridge ).

Every monad arises from some adjunction — in fact, typically from many adjunctions — in the above fashion.

Every time reasonable suspicion arises, the police are obliged to intervene under a zero tolerance strategy even though mere police intuition is legally insufficient.

Every great Culture begins with a religious trend that arises in the countryside, is carried through to the cultural cities, and ends in materialism in the world-cities.

Every monad arises from some adjunction, in fact typically from many adjunctions.

Every integer 2g ' 2g matrix with < sup >*</ sup > arises as the Seifert matrix of a knot with genus g Seifert surface.

Every few minutes she would awaken for a moment to review things: Stowey, yes, was on his way south, and the two boys were away in school, and nothing was burning on the stove, and Lucretia was coming for dinner and bringing three guests of hers.

Every cleric in Holy Orders and every member of a religious order must publicly join in or privately read aloud ( i. e. using the lips as well as the eyes — it takes about two hours in this way ) the whole of the Breviary services allotted for each day.

" More immediately, though, he called for a massive build-up of U. S. arms production: " Every realist knows that the democratic way of life is at this moment being ' directly assailed in every part of the world … The need of the moment is that our actions and our policy should be devoted primarily — almost exclusively — to meeting this foreign peril.

Every positive integer n > 1 can be represented in exactly one way as a product of prime powers:

# Moral law of karma: Every action ( by way of body, speech, and mind ) will have karmic results ( a. k. a. reaction ).

* Every finite topological space gives rise to a preorder on its points, in which x ≤ y if and only if x belongs to every neighborhood of y, and every finite preorder can be formed as the specialization preorder of a topological space in this way.

Every view of reality that is introduced in the story is later derided in some way, whether that view is traditional or iconoclastic.

Every ear attends ... his eloquent words move the heart, convince the reason, and tell the weak and wavering which way to go.

Every distinct map projection distorts in a distinct way.

Every continent has at least one such notable institute, with North America and Europe leading the way forward.

; Every Day / A Heart Full Of Love ( Reprise ): Valjean arrives in the middle of a love scene between Cosette and Marius and decides not to stand in the way of their happiness.

" I might easily have written this story in the traditional manner [...] Every novelist knows the recipe [...] It is not very difficult to follow a simple, chronological scheme which the critics will understand [...] But I, after all, am trying to tell the story of this Chapelizod family in a new way.

Every group has a presentation, and in fact many different presentations ; a presentation is often the most compact way of describing the structure of the group.

* Émile Coué ( 1857 – 1926 ) pharmacist, hypnotist, and creator of La méthode Coué (" Every day, in every way, I'm getting better and better ').

§ 1: " Every subject expects from the territorial prince security and protection, so it is the duty of the territorial prince, the rights of subjects to determine clearly and to guide the way of the actions how it is needed by universal and special prosperity.

Every smooth manifold defined in this way has a natural diffeology, for which the plots correspond to the smooth maps from open subsets of R < sup > n </ sup > to the manifold.

Every day is a new way.

Every man being organized in a particular way has, of necessity, an aim, the fulfilment of which is good ; and he has faculties for accomplishing it, directed by reason.

Every enterprise constrains behavior in some way, and this is closely related to constraints on what data may or may not be updated.

Every sigma-ideal on X can be recovered in this way by placing a suitable measure on X, although the measure may be rather pathological.

During his career as writer and while living in the mountains, Muir continued to experience the " presence of the divine in nature ," writes Holmes From Travels in Alaska: " Every particle of rock or water or air has God by its side leading it the way it should go ; The clearest way into the Universe is through a forest wilderness ; In God's wildness is the hope of the world.

Every Boolean algebra can be obtained in this way from a suitable topological space: see Stone's representation theorem for Boolean algebras.

Every side in AIK's group had the potential of going all the way: Arsenal, Barcelona och Fiorentina.

Every time I closed my eyes, I saw Gray Eyes rushing at me with a knife.

Every movement she made seemed unnecessarily noisy.

`` Every last one of you.

Every plane that could fly was sent into the air.

Every so often the diminishing sound of a car came under the trailer as it slowed down for the wreck then speeded up again as it got clear.

Every so often he turned the knife.

Every bone and muscle in his body showed, but he did not give the appearance of starving.

Every path from back door to barn was covered by a grape-arbor, and every yard had its fruit trees.

Every morning early, in the summer, we searched the trunks of the trees as high as we could reach for the locust shells, carefully detached their hooked claws from the bark where they hung, and stabled them, a weird faery herd, in an angle between the high roots of the tulip tree, where no grass grew in the dense shade.

Every slight sound that rose against that pressure fell away again, crushed beneath it.

They give strict interpretation to William James' statement that `` Every idea that enters the mind tends to express itself ''.

Every morning contingents of prisoners would be sent out to labor in nearby factories.

If nothing else, at least two good songs came out of the project, `` Out Of This World '' and `` June Comes Around Every Year ''.

Every day, when the President took his nap, Rob Roy would stretch out on the window seat near him, like a perfect gentleman, and stare thoughtfully out the window, or he would take a little nap himself.

Every First Family seems to have one couple upon whom it relies for true friendship.

Every letter answers itself in a couple of weeks ''.

Every recorded request by Thomas for a delay in a flank movement or an advance was to gain time to take care of his horses.

Every chance I got I left the hotel to visit Lilly.

Every man who dabbles in the market to make a little easy money on the side and suffers losses could at the time hardly face his wife who was wondering how her husband could be so dumb.

Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.

Sir -- Every resident of this city should visit the Newark Museum and see the exhibit `` Our Changing Skyline in Newark ''.

Every soldier in the army has, somewhere, relatives who are close to starvation.

Every woman has had the experience of saying no when she meant yes, and saying yes when she meant no.

Every eye was on him as he began to speak.

Every time he moved or said something, the chair creaked again.