Page "Length of a module" ¶ 22
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## Some Related Sentences

Every and module
Every module over a division ring has a basis ; linear maps between finite-dimensional modules over a division ring can be described by matrices, and the Gaussian elimination algorithm remains applicable.
Every library module has at least two source files: a definitions file specifying the library's interface plus one or more program files specifying the implementation of the procedures in the interface.
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.
Every simple module is indecomposable, but the converse is in general not true.
Every simple module is cyclic, that is it is generated by one element.
Every injective module can be decomposed as direct sum of indecomposable injective modules.
Every vector space is free, and the free vector space on a set is a special case of a free module on a set.
* Every module over a field or skew field is projective ( even free ).
* Every projective module is flat.
Every module possesses a projective resolution.
Every module of the form H * is algebraically compact.
Every indecomposable algebraically compact module has a local endomorphism ring.
* Every module M has an injective hull.
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 simple module is indecomposable.
Every ring which is semisimple as a module over itself has zero Jacobson radical, but not every ring with zero Jacobson radical is semisimple as a module over itself.
* Every module can focus on what it is designed for.
Every superfield, i. e. a field that depends on all coordinates of the superspace ( or in other words, an element of a module of the algebra of functions over superspace ), may be expanded with respect to the new fermionic coordinates.

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 endomorphism of M is either nilpotent or invertible.
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 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 has
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 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 calculation has been made independently by two workers and checked by one of the editors.
Every retiring person has a different situation facing him.
Every family of Riviera Presbyterian Church has been asked to read the Bible and pray together daily during National Christian Family Week and to undertake one project in which all members of the family participate.
Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.
`` Every woman in the block has tried that ''.
: Every set has a choice function.
Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set.
** Every surjective function has a right inverse.
** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
** Antichain principle: Every partially ordered set has a maximal antichain.
** Every vector space has a basis.
* Every small category has a skeleton.
* Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint ( the Freyd adjoint functor theorem ).
** Every field has an algebraic closure.
** Every field extension has a transcendence basis.
** Every Tychonoff space has a Stone – Čech compactification.
Every unit of length has a corresponding unit of area, namely the area of a square with the given side length.
Every field has an algebraic extension which is algebraically closed ( called its algebraic closure ), but proving this in general requires some form of the axiom of choice.
Every ATM cell has an 8-or 12-bit Virtual Path Identifier ( VPI ) and 16-bit Virtual Channel Identifier ( VCI ) pair defined in its header.

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