Page "Schur's lemma" ¶ 17
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## Some Related Sentences

Every and endomorphism
Every indecomposable algebraically compact module has a local endomorphism ring.
Consider a Lie algebra g over a field K. Every element x of g defines the adjoint endomorphism ad ( x ) ( also written as ad < sub > x </ sub >) of g with the help of the Lie bracket, as

Every and M
* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =
Every song they wrote was written with an eye toward giving it " deep hidden meaning " or D. H. M.
* In any ring R, a maximal ideal is an ideal M that is maximal in the set of all proper ideals of R, i. e. M is contained in exactly 2 ideals of R, namely M itself and the entire ring R. Every maximal ideal is in fact prime.
Every smooth ( or differentiable ) map φ: M → N between smooth ( or differentiable ) manifolds induces natural linear maps between the corresponding tangent spaces:
Every measurable cardinal κ is a 0-huge cardinal because < sup > κ </ sup > MM, that is, every function from κ to M is in M. Consequently, V < sub > κ + 1 </ sub >⊂ M.
# " 5. 06 A. M. ( Every Strangers ' Eyes )"
: Every countable theory which is satisfiable in a model M, is satisfiable in a countable substructure of M.
* Siegal, M., Cornell Feline Health Center ( Editors ) ( 1989 ) The Cornell Book of Cats: A Comprehensive Medical Reference for Every Cat and Kitten.
Every year about 5000 applications are received, out of which about 300 students ( around 150 in each year ) are enrolled in the 2 year full time M. Tech.
Every hyperkähler manifold M has a 2-sphere of complex structures ( i. e. integrable almost complex structures ) with respect to which the metric is Kähler.
* Every module M has an injective hull.
Every finite-length module M has a composition series, and the length of every such composition series is equal to the length of M.
Every year the department admits students for it M. A / MSc., M. Phil and Ph. D courses.
* Every direct summand of M is pure in M. Consequently, every subspace of a vector space over a field is pure.

Every and is
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.
Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.
Every taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.
Every single problem touched on thus far is related to good marketing planning.
Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.
Every dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.
Every man in every one of these houses is a Night Rider.
Every library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.
Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.
The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.
** Every infinite game in which is a Borel subset of Baire space is determined.
Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).
Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.
Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.
Every year, on the last Sunday in April, there is an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth.
Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.

Every and either
Every two equivalence classes and are either equal or disjoint.
Hilbert's example: " the assertion that either there are only finitely many prime numbers or there are infinitely many " ( quoted in Davis 2000: 97 ); and Brouwer's: " Every mathematical species is either finite or infinite.
Every morpheme can be classified as either free or bound.
* Every formal address or message " to the nation " or to either or both Houses of the Oireachtas must have prior approval of the Government.
Every karma produces a result which must be experienced either in this or some future life.
Belkis Lora, a relative of a passenger on the crashed flight, said " Every Dominican in New York has either taken that flight or knows someone who has.
" Aside from merely disputing readings of his own work, however, in " Letter on ' Humanism ,'" Heidegger asserts that " Every humanism is either grounded in a metaphysics or is itself made to be the ground of one.
The following propositions all imply one another: " Every object is either black or not a raven ", " Every Raven is black ", and " Every non-black object is a non-raven.
Every resultant is either a sum or a difference of the co-operant forces ; their sum, when their directions are the same -- their difference, when their directions are contrary.
Every Duke thereafter has either died without heirs or succeeded to the Crown, and so has not been able to leave the Royal Family.
Every French noun has a grammatical gender, either masculine or feminine.
Every destination in the topology table can be marked either as " Passive ", which is the state when the routing has stabilized and the router knows the route to the destination, or " Active " when the topology has changed and the router is in the process of ( actively ) updating its route to that destination.
Every map that is injective, continuous and either open or closed is an embedding ; however there are also embeddings which are neither open nor closed.
Every car uses either a 5. 0 L Ford " Boss 302 " SVO or a 5. 0 L Chevrolet small block race-engine ( depending on the make )-capable of producing between 460 and 485 kW ( 620 — 650 bhp ) of power, but generally quoted as a little over 450 kW ( 600 bhp ) in race trim.
Other sauces are either prepared from scratch, or are variations on a basic curry sauce :< ref ><" Every restaurant has a large pan of this sauce always at hand, with the recipe varying only slightly from Chef to Chef.
Every day is spent either in study of scriptures or meditation or teaching to lay people.
Concerning the role of clave in salsa music, Charley Gerard states: “ The clave feeling is in the music whether or not the claves are actually being played .” Every ostinato part which spans a cycle of four main beats, has a specific alignment with clave, and expresses the rhythmic qualities of clave either explicitly or implicitly.
Every stream from either side of the valley has its large terraces to correspond with those of the Passumpsic River.
Every even-numbered year either two or three members are elected by the people to serve a four-year term.
' Every year its either held in Baldwin or Franklin.
Every acre was owned by someone, either a private individual or by government in the form of the Crown.
The International Committee of the Red Cross 1958 Commentary on 1949 Geneva Convention IV Relative to the Protection of Civilian Persons in Time of War states: " Every person in enemy hands must have some status under international law: he is either a prisoner of war and, as such, covered by the Third Convention, a civilian covered by the Fourth Convention, or again, a member of the medical personnel of the armed forces who is covered by the First Convention.

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