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Every free abelian group has a rank defined as the cardinality of a basis.
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good, is more or less toxic and irritating to a wounded surface ; as a result, in surgery, the antiseptic method has been replaced by aseptic method, which is preventative in nature and relies on keeping free from the invasion of bacteria rather than destroying them when present.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.