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Every finitely-generated R-module is a direct sum of these.
Some Related Sentences
Every and finitely-generated
A finitely-generated abelian group is indecomposable if and only if it is isomorphic to Z or to a factor group of the form for some prime number p and some positive integer n. Every finitely-generated abelian group is a direct sum of ( finitely many ) indecomposable abelian groups.
Every and R-module
Every simple R-module is isomorphic to a quotient R / m where m is a maximal right ideal of R. By the above paragraph, any quotient R / m is a simple module.
This is up to isomorphism the only indecomposable module over R. Every left R-module is a direct sum of ( finitely or infinitely many ) copies of this module K < sup > n </ sup >.
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 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 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 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 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 direct
Every McIntosh apple has a direct lineage to a single tree discovered in 1796 by John McIntosh on his farm in Dundela, a hamlet near Morrisburg, in Dundas County, Ontario, Canada.
Every aspect of the methodology advocated in NKS is optimized to make experimentation as direct, easy, and meaningful as possible — while maximizing the chances that the experiment will do something unexpected.
Every adverse effect is the result of a set of direct factors, the absence of any one of which would have resulted in the effect having been different than it was.
Every winter, second year students at HMS write, direct, and perform a full-length musical parody of Harvard, their professors, and themselves.
As stated by the WHO in its 2005 World Health Report " Make Every Mother and Child Count ", the major causes of maternal deaths are: severe bleeding / hemorrhage ( 25 %), infections ( 13 %), unsafe abortions ( 13 %), eclampsia ( 12 %), obstructed labour ( 8 %), other direct causes ( 8 %), and indirect causes ( 20 %).
Every other year, they have a repertoire of student-directed plays, in which students apply to direct a play of their choice.
* Every direct summand of M is pure in M. Consequently, every subspace of a vector space over a field is pure.
Every formally real Jordan algebra can be written as a direct sum of so-called simple ones, which are not themselves direct sums in a nontrivial way.
The key amendment to the Criminal Code reads as follows: " 217. 1 Every one who undertakes, or has the authority, to direct how another person does work or performs a task is under a legal duty to take reasonable steps to prevent bodily harm to that person, or any other person, arising from that work or task.
Every international success was presented as a direct result of the righteousness of the communist rule and ideology.
# Every submodule of M is a direct summand: for every submodule N of M, there is a complement P such that M = N ⊕ P.
Every quantum field theory satisfying certain technical assumptions about its S-matrix that has non-trivial interactions can only have a symmetry Lie algebra which is always a direct product of the Poincaré group and an internal group if there is a mass gap: no mixing between these two is possible.
Every member therefore has a direct vote on whether or not the pay of their national officers and staff will be increased.
* Every serial between The Leisure Hive and The Five Doctors is linked in some way, either directly leading from one storyline to the next, or through direct reference.
Every Columbia series alternated between the White and McCollum units, allowing Bernds to direct the other Columbia comedians: Shemp Howard.
* Provide a Stake in the Outcome: Every employee should have a direct stake in the company's success-and in the risk of failure