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 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 finite-length module M has a composition series, and the length of every such composition series is equal to the length of M.

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 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 information exchange between living organisms — i. e. transmission of signals that involve a living sender and receiver can be considered a form of communication ; and even primitive creatures such as corals are competent to communicate.

Every context-sensitive grammar which does not generate the empty string can be transformed into an equivalent one in Kuroda normal form.

* Every pair of congruence relations for an unknown integer x, of the form x ≡ k ( mod a ) and x ≡ l ( mod b ), has a solution, as stated by the Chinese remainder theorem ; in fact the solutions are described by a single congruence relation modulo ab.

Every grammar in Chomsky normal form is context-free, and conversely, every context-free grammar can be transformed into an equivalent one which is in Chomsky normal form.

Every summer form mid-June to early July, The Heart of America Shakespeare Festival has a production at Southmoreland Park near the Nelson-Atkins Museum.

Every RFC is submitted as plain ASCII text and is published in that form, but may also be available in other formats.

Every form is the delimitation of a surface by another one ; it possesses an inner content, the effect it produces on one who looks at it attentively.

Every synset contains a group of synonymous words or collocations ( a collocation is a sequence of words that go together to form a specific meaning, such as " car pool "); different senses of a word are in different synsets.

Every twin prime pair except ( 3, 5 ) is of the form ( 6n − 1, 6n + 1 ) for some natural number n, and with the exception of < var > n </ var > = 1, < var > n </ var > must end in 0, 2, 3, 5, 7, or 8.

Every dual number has the form z = a + bε with a and b uniquely determined real numbers.

" Every adult had to fill out a form detailing his or her past.

Every context-free grammar can be transformed into an equivalent grammar in Greibach normal form.

Every religion on Earth see there god in the form of light, the spread of some beam light, Islam noor, Christian rays of light it nothing but it Shiva.

Every one of these calendars has a year of 365 days, which is occasionally extended by adding an extra day to form a leap year, a method called " intercalation ", the inserted day being " intercalary ".

In Sikhism, Every soul who have taken form or born on earth is called Avtar.

Long created the Share Our Wealth program in 1934 with the motto " Every Man a King ", proposing new wealth redistribution measures in the form of a net asset tax on corporations and individuals to curb the poverty and homelessness endemic nationwide during the Great Depression.

Every acre was owned by someone, either a private individual or by government in the form of the Crown.

Every decision made by three of these " deputations " — and in each of them the lower clergy formed the majority — received ratification for the sake of form in general congregation, and if necessary led to decrees promulgated in session.

The title " Every Good Boy Deserves Favour " was borrowed, tongue-in-cheek, from a mnemonic used to remember the musical notes that form the lines of the treble clef: EGBDF.

Ongoing acrimony between the brothers, however, led to Tommy Dorsey's walking out to form his own band in 1935, just as the orchestra was having a hit with " Every Little Moment.

Every building in Regent Street is protected as a Listed Building, at least Grade II status, and together they form the Regent Street Conservation Area.

Every action has some impact in the environment, and the environment provides feedback in the form of rewards that guides the learning algorithm.

Every Wake Forest undergraduate student who lives on campus is required to sign up for some form of a meal plan in coordination with Aramark.