[permalink] [id link]

Every free abelian group has a rank defined as the cardinality of a basis.

from
Wikipedia

## Some Related Sentences

Every and free

__Every__

__free__man, born in lawful wedlock, and neither excommunicate nor outlaw, was eligible for membership

**.**

__Every__other province had

**the**freedom to regulate

**the**religious question

**as**it wished, although

**the**Union stated every person should be

__free__in

**the**choice

**of**his personal religion and no person should be prosecuted based on his or her religious choice

**.**

The Body

**of**Liberties adopted in 1641 by**the**Massachusetts Bay colonists states, “__Every__married woman shall be__free__from bodily correction or stripes by her husband, unless it be in his own defense from her assault .” In**the**United States, legal decisions in Mississippi ( 1824 ) and North Carolina ( 1868 and 1874 ) make reference to — and reject — an unnamed " old doctrine " or " ancient law " by which**a**man was allowed to beat his wife with**a**stick no wider than his thumb**.**__Every__antiseptic, however good, is more or less toxic and irritating to

**a**wounded surface ;

**as**

**a**result, in surgery,

**the**antiseptic method

**has**been replaced by aseptic method, which is preventative in nature and relies on keeping

__free__from

**the**invasion

**of**bacteria rather than destroying them when present

**.**

* The Empty Space:

__Every__Friday**the**Students ' Union hosts**a**live music venue in The Empty Space, attended by students for__free__( this was canceled in 2011 due to changes installed by**the**69th Student Legislative Council ).
*

__Every__August**the**residents**of**Sleepy Eye host**the**annual " Corn Days " event, where__free__buttered corn is provided,**as**well**as**live music,**a**flea market, parade, and various other events**.**
*

__Every____free__**abelian****group**is torsion-free, but**the**converse is not true,**as**is shown by**the**additive**group****of****the**rational numbers Q**.**__Every__week

**of**

**the**Michaelmas and Lent terms, and twice in Easter term, Churchill is host to Pav,

**a**music event unusual for Cambridge events in that it is

__free__and open to all university members

**.**

__Every__summer,

**a**

__free__tourist train in

**the**city centre connects

**the**ancient parts

**of**

**the**city with

**the**government district

**.**

__Every__town wanted to be

**a**railway centre, and

**the**government had great confidence in

**the**ability

**of**

**the**

__free__market to provide low freight rates to

**the**province's farmers provided sufficient charters were issued to competing companies

**.**

__Every__subgroup

**of**

**a**

__free__

**abelian**

**group**is itself

__free__

**abelian**, which is important for

**the**description

**of**

**a**general

**abelian**

**group**

**as**

**a**cokernel

**of**

**a**homomorphism between

__free__

**abelian**groups

**.**

__Every__month Hustler is mailed, uninvited and for

__free__, to some

**of**

**the**offices

**of**Members

**of**

**the**United States Congress

**.**

__Every__Riemann surface is

**the**quotient

**of**

**a**

__free__, proper and holomorphic action

**of**

**a**discrete

**group**on its universal covering and this universal covering is holomorphically isomorphic ( one also says: " conformally equivalent ") to one

**of**

**the**following:

__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__Ontario resident with his or her primary and permanent home in Ontario is entitled to access emergency and preventive medical care ( although Bariatric surgery in many cases is not covered ) under OHIP

__free__

**of**charge

**.**

Every and abelian

__Every__algebraic curve C

**of**genus g ≥ 1 is associated with an

__abelian__variety J

**of**dimension g, by means

**of**an analytic map

**of**C into J

**.**

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__

__abelian__category is an exact category if we just use

**the**standard interpretation

**of**" exact ".

Every and group

Group actions / representations:

__Every____group__G can be considered**as****a**category with**a**single object whose morphisms are**the**elements**of**G**.**A functor from G to Set is then nothing but**a**__group__action**of**G on**a**particular set, i**.**e**.****a**G-set**.**__Every__galaxy

**of**sufficient mass in

**the**Local Group

**has**an associated

__group__

**of**globular clusters, and almost every large galaxy surveyed

**has**been found to possess

**a**system

**of**globular clusters

**.**

*

__Every__Lie__group__is parallelizable, and hence an orientable manifold ( there is**a**bundle isomorphism between its tangent bundle and**the**product**of**itself with**the**tangent space at**the**identity )__Every__instrumental

__group__( or section )

**has**

**a**principal who is generally responsible for leading

**the**

__group__and playing orchestral solos

**.**

*

__Every__closed subgroup**of****a**profinite__group__is itself profinite ;**the**topology arising from**the**profiniteness agrees with**the**subspace topology**.**
While he admits

**the**existence**of**caste-based discrimination, he writes that "__Every__social__group__cannot be regarded**as****a**race simply because we want to protect it against prejudice and discrimination ".__Every__summer

**the**

__group__gathers in Newport, RI for week long dance training, seaside teas, and evenings enjoying

**the**splendors

**of**

**the**Gilded Age

**.**

*

__Every__finitely generated__group__with**a**recursively enumerable presentation and insoluble word problem is**a**subgroup**of****a**finitely presented__group__with insoluble word problem__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__

__group__can be trivially made into

**a**topological

__group__by considering it with

**the**discrete topology ; such groups are called discrete groups

**.**

__Every__topological

__group__can be viewed

**as**

**a**uniform space in two ways ;

**the**left uniformity turns all left multiplications into uniformly continuous maps while

**the**right uniformity turns all right multiplications into uniformly continuous maps

**.**

__Every__subgroup

**of**

**a**topological

__group__is itself

**a**topological

__group__when given

**the**subspace topology

**.**

__Every__ten years, when

**the**general census

**of**population takes place, each citizen

**has**to declare which linguistic

__group__they belong or want to be aggregated to

**.**

0.196 seconds.