[permalink] [id link]

Conversely, given a left kG module M, then M is a k vector space, and multiplication with an element g of G yields a k-linear automorphism of M ( since g is invertible in kG ), which describes a group homomorphism G → GL ( M ).

from
Wikipedia

## Some Related Sentences

Conversely and given

__Conversely__

**,**if

**a**Boolean ring A

**is**

__given__

**,**we can turn it into

**a**Boolean algebra by defining x ∨ y := x + y +

**(**x · y )

**and**x ∧ y := x · y.

__Conversely__

**,**there are other stars that never rise above the horizon

**,**as seen from any

__given__point on the Earth's surface

**(**except exactly on the equator

**).**

__Conversely__

**,**

__given__

**a**groupoid

**G**

**in**the algebraic sense

**,**let

**G**< sub > 0 </ sub > be the set

**of**all elements

**of**the form x * x < sup >− 1 </ sup >

**with**x varying through

**G**

**and**define

**G**

**(**x * x < sup >-1 </ sup >, y * y < sup >-1 </ sup >) as the set

**of**all elements f such that y * y < sup >-1 </ sup > * f * x * x < sup >-1 </ sup > exists.

__Conversely__

**,**

__given__central idempotents

**a**< sub > 1 </ sub >,...,

**a**< sub > n </ sub >

**in**R that are pairwise orthogonal

**and**have sum 1

**,**

**then**R

**is**the direct sum

**of**the rings Ra < sub > 1 </ sub >,…, Ra < sub > n </ sub >.

Given

**a**field ordering ≤ as**in**Def 1**,**the elements such that x ≥ 0 forms**a**positive cone**of**F.__Conversely__**,**__given__**a**positive cone P**of**F as**in**Def 2**,**one can associate**a**total ordering ≤< sub > P </ sub > by setting x ≤ y to mean y − x ∈ P. This total ordering ≤< sub > P </ sub > satisfies the properties**of**Def 1.__Conversely__

**,**only the wiki users interested

**in**

**a**

__given__project need look at its associated wiki pages

**,**

**in**contrast to high-traffic mailing lists

**which**may burden subscribers

**with**many messages

**,**regardless

**of**their relevance.

__Conversely__

**,**

__given__

**a**harmonic function

**,**it

**is**the real part

**of**

**an**analytic function

**,**

**(**at least locally

**).**

Each convex set containing X must

**(**by the assumption that it**is**convex ) contain all convex combinations**of**points**in**X**,**so the set**of**all convex combinations**is**contained**in**the intersection**of**all convex sets containing X.__Conversely__**,**the set**of**all convex combinations**is**itself**a**convex set containing X**,**so it also contains the intersection**of**all convex sets containing X**,****and**therefore the sets__given__by these two definitions must be equal.__Conversely__

**,**surveys conducted among living donors postoperatively

**and**

**in**

**a**period

**of**five years following the procedure have shown extreme regret

**in**

**a**majority

**of**the donors

**,**who said that

__given__the chance to repeat the procedure

**,**they would not.

__Conversely__

**,**

__given__

**an**ordered tree

**,**

**and**conventionally draw the root at the top

**,**

**then**the child nodes

**in**

**an**ordered tree can be drawn left-to-right

**,**yielding

**an**essentially unique planar embedding

**(**up to embedded homotopy

**,**i. e., moving the edges

**and**nodes without crossing

**).**

__Conversely__

**,**the influence

**of**the data at any

__given__point on the initial line propagates

**with**the finite velocity c: there

**is**no effect outside

**a**triangle through that point whose sides are characteristic curves.

__Conversely__

**,**

__given__any harmonic function

**in**two dimensions

**,**it

**is**the real part

**of**

**an**analytic function

**,**at least locally.

__Conversely__

**,**if

**(**A

**,**m

**,**e

**,**inv )

**is**

**a**

**group**object

**in**one

**of**those categories

**,**

**then**m necessarily coincides

**with**the

__given__operation on A

**,**e

**is**the inclusion

**of**the

__given__identity

**element**on A

**,**inv

**is**the inversion operation

**and**A

**with**the

__given__operation

**is**

**an**abelian

**group**.

__Conversely__

**,**if the Turing Machine

**is**expected polynomial-time

**(**for any

__given__x

**),**

**then**

**a**considerable fraction

**of**the runs must be polynomial-time bounded

**,**

**and**the coin sequence used

**in**such

**a**run will be

**a**witness.

__Conversely__

**,**

__given__any ring

**,**we can form

**a**category by taking objects A < sub > n </ sub > indexed by the set

**of**natural numbers

**(**including zero )

**and**letting the hom-set

**of**morphisms from to be the set of-by-matrices over

**,**

**and**where composition

**is**

__given__by matrix

**multiplication**.

__Conversely__

**,**it

**is**hard to believe

**,**

__given__the length

**and**intensity

**of**the struggle between Máel Sechnaill

**and**Brian

**,**that the High King would surrender his title without

**a**fight.

__Conversely__

**,**

**an**algorithm to test for solvability

**in**arbitrary integers could be used to test

**a**

__given__equation for solvability

**in**natural numbers by applying that supposed algorithm to the equation obtained from the

__given__equation by replacing each unknown by the sum

**of**the squares

**of**four new unknowns.

__Conversely__

**,**

**a**disease that

**is**easily transmitted but has

**a**short duration might spread widely during 2002 but

**is**likely to have

**a**low prevalence at any

__given__point

**in**2003

**(**due to its short duration ) but

**a**high incidence during 2002

**(**as many people develop the disease

**).**

Conversely and left

__Conversely__the equilibrium position

**is**said to be " far to the

__left__" if hardly any product

**is**formed from the reactants.

__Conversely__women take one step backwards

**and**

**then**slide to the

__left__passing behind

**of**their neighbour

**,**

**then**step forwards

**and**slide right

**in**front

**of**their neighbour.

__Conversely__

**,**if F

**is**

__left__adjoint to

**G**

**,**

**and**

**G**

**is**naturally isomorphic to

**G**′

**then**F

**is**also

__left__adjoint to

**G**′.

As stated earlier

**,****an**adjunction between categories C**and**D gives rise to**a**family**of**universal morphisms**,**one for each object**in**C**and**one for each object**in**D.__Conversely__**,**if there exists**a**universal morphism to**a**functor**G**: C**→**D from every object**of**D**,****then****G**has**a**__left__adjoint.__Conversely__

**,**

**a**natural

**,**military or ecological disaster might move the PPF to the

__left__

**,**

**in**response to

**a**reduction

**in**

**an**economy's productivity.

__Conversely__

**,**the pulmonary veins

**,**carrying blood from the lungs to the

__left__atrium

**of**the heart

**,**are the only veins carrying oxygenated blood.

__Conversely__

**,**if the

__left__eye

**is**covered

**,**the pendulum would appear to be revolving clockwise-from-top

**,**appearing closer as it swings toward the

__left__

**and**farther as it swings toward the right.

__Conversely__

**,**

**in**Japan-where the Matrix

**is**treated simply as

**a**reservoir

**of**pure energy-the shell was

__left__hidden on Earth to slowly recharge its depleted energy.

__Conversely__the United Empire Loyalists

__left__what was to be the United States

**and**moved North to remain under British rule.

__Conversely__

**,**his sister wrote

**in**the December 1952 issue

**of**Modern Screen Magazine that he

__left__Norma Jeane because she decided to pursue modeling

**,**

**and**he didn't like the attention it created.

Conversely and module

__Conversely__

**,**if

**a**highest weight

__module__

**is**integrable

**,**

**then**its highest weight

**vector**v satisfies

**,**where are complex numbers such that

A sublinear modulus

**of**continuity can easily found for any uniformly function**which****is****a**bounded perturbations**of****a**Lipschitz function: if**is****a**uniformly continuous function**with**modulus**of**continuity**,****and****is****a**Lipschitz function**with**uniform distance from**,****then**admits the sublinear__module__**of**continuity__Conversely__**,**at least for real-valued functions**,**any bounded**,**uniformly continuous perturbation**of****a**Lipschitz function**is****a**special uniformly continuous function ; indeed more**is**true as shown below.__Conversely__

**,**different types

**of**hulks exist including one that simply " swallows " the probe without yielding

**a**

__module__

**,**requiring the player to purchase

**a**new probe

**(**

**and**possibly sell useful modules to raise the required funds

**).**

__Conversely__

**,**

**a**PXI

__module__installed

**in**

**a**CompactPCI chassis would not utilize the additional clocking

**and**triggering features

**of**the PXI

__module__.

0.181 seconds.