Examples of using Finitely generated in English and their translations into Portuguese
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it cannot be finitely generated.
If we restrict ourselves to finitely generated groups, we can consider the following arrangement of classes of groups: cyclic< abelian< nilpotent< supersolvable< polycyclic< solvable< finitely generated group.
gupta-sidki groups play fundamental role in modern group theory because they are natural examples of self-similar finitely generated periodic groups.
If"R" is a left-noetherian ring, then the category of finitely generated left modules over"R" is abelian.
we are interested in studying the category modA of finitely generated right A-modules where A is an artin algebra.
is the nilradical of A. Every finitely generated module over A has finite length.(see
While it is true that every quotient of a finitely generated group is finitely generated(simply take the images of the generators in the quotient), a subgroup of a finitely generated group need not be finitely generated.
an arbitrary positive characteristic, giving an example of finitely generated restricted lie algebra with a nil p-mapping.
Every finite group is finitely generated since⟨G⟩ G. The integers under addition are an example of an infinite group which is finitely generated by both 1 and -1, but the group of rationals under addition cannot be finitely generated.
which determines a condition on the integral domain r so that every finitely generated torsion free module is written as a direct sum of modules of rank 1.
that is, we can form a tensor product of a finitely generated abelian group"G" and any object"A" of A.
The integers under addition are an example of an infinite group which is finitely generated by both 1 and -1, but the group of rationals under addition cannot be finitely generated.
as well as the case of finitely generated groups and notions of completion,
the authors proved that if$a$ is finitely generated, then its pi-exponent,
where authors showed that for a large class of finitely generated groups the generic time complexity of some classical decision problems from combinatorial group theory,
His most famous result is that the ring of invariants of binary forms of fixed degree is finitely generated.
then we can remove the requirement that"G" be finitely generated; most generally,
Makar-limanov's conjecture states that if a division ring d is finitely generated and infinite dimensional over its center k then d contains a free k-subalgebra of rank 2.
To see this, take a generating set for the(finitely generated) normal subgroup and quotient: then the generators for the normal subgroup, together with preimages of the generators for the quotient, generate the group.
In this work we present a proof of the remarkable theorem of mordell which states that the group of the rational points of an elliptic curve defined over the field of rational numbers is finitely generated.
