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Some Related Sentences
ring and is

Our new large-package
ring twister for glass fiber yarns
is performing well
in our customers' mills
.

If you walk into
the ring because it
is fun to show your dog
, he will feel it and give you a good performance!!

`` The reason you are
in the ring today
is to show your ability to present to any judge
the most attractive picture
of your dog that
the skillful use
of your aids can produce
.
This is the tale
of one John Enright
, an American who has accidentally killed a man
in the prize
ring and
is now trying to forget about it
in a quiet place where he may become a quiet man
.

`` He has married me
with a
ring of bright water ''
, begins
the Kathleen Raine poem from which Maxwell takes his title
, and it
is this mystic bond between
the human and natural world that
the author conveys
.

Many theorems which are provable using choice are
of an elegant general character:
every ideal
in a
ring is contained
in a maximal ideal
, every vector space has a basis
, and
every product
of compact spaces
is compact
.

The field F
is algebraically closed if and only if
the only irreducible polynomials
in the polynomial
ring F are those
of degree one
.

The ceremony
of such a blessing
is similar
in some aspects to
the consecration
of a bishop
, with the new abbot being presented
with the mitre
, the ring, and
the crosier as symbols
of office and receiving
the laying on
of hands and blessing from
the celebrant
.

The sum
, difference
, product and quotient
of two algebraic numbers
is again algebraic
( this fact can be demonstrated using
the resultant ), and
the algebraic numbers therefore form a field
, sometimes denoted by
A ( which may also denote
the adele
ring ) or < span style =" text-decoration: overline ;"> Q </ span >.

If K
is a number field
, its
ring of integers
is the subring
of algebraic integers
in K
, and
is frequently denoted as O < sub > K </ sub >.

In
the context
of abstract algebra
, for example
, a mathematical
object is an algebraic structure such as a group
, ring, or vector space
.

Generally speaking
, negation
is an automorphism
of any abelian group
, but not
of a
ring or field
.

*
A field automorphism
is a bijective
ring homomorphism from a field to itself
.

The same definition holds
in any unital
ring or algebra where a
is any invertible element
.

The configuration
of six carbon atoms
in aromatic compounds
is known as a benzene
ring, after
the simplest possible such hydrocarbon
, benzene
.

The structure
is also illustrated as a circle around
the inside
of the ring to show six electrons floating around
in delocalized molecular orbitals
the size
of the ring itself
.

In aromatic substitution one substituent on
the arene
ring, usually hydrogen
, is replaced by another substituent
.

When there
is more than one substituent present on
the ring, their spatial relationship becomes important for which
the arene substitution patterns ortho
, meta
, and para are devised
.
This is seen
in, for example
, phenol
( C < sub > 6 </ sub > H < sub > 5 </ sub >- OH ), which
is acidic at
the hydroxyl
( OH ), since a charge on this oxygen
( alkoxide-O < sup >–</ sup >)
is partially delocalized into
the benzene
ring.
ring and endomorphism

*
endomorphism ring

* Given an R-module M
, the endomorphism ring of M
, denoted End < sub > R </ sub >( M
) is an R-algebra by defining
( r · φ )( x
) = r · φ
( x ).

In general
, if R
is a
ring and S
is a simple module over R
, then
, by Schur's lemma
, the endomorphism ring of S
is a division
ring ;
every division
ring arises
in this fashion from
some simple module
.

In
the case when
the endomorphism ring, where each
endomorphism arises as left multiplication by a fixed
ring element
.

If a
is an idempotent
of the endomorphism ring End < sub > R </ sub >( M ), then
the endomorphism is an R module involution
of M
. That
is, f
is an R homomorphism such that f < sup > 2 </ sup >
is the identity endomorphism of M
.

Consequently
the endomorphism ring of any simple module
is a division
ring.

For example
, the Z-module Q
is not simple
, but its
endomorphism ring is isomorphic to
the field Q
.

For example
, the Fitting lemma shows that
the endomorphism ring of a finite length indecomposable module
is a local
ring, so that
the strong Krull-Schmidt theorem holds and
the category of finite length modules
is a Krull-Schmidt
category.

Focusing on a single
object A in a
preadditive category, these facts say that
the endomorphism hom-set Hom
( A, A ) is a
ring, if we define multiplication
in the ring to be composition
.
ring and .

In
the brief moment I had to talk to them before I took my post on
the ring of defenses
, I indicated I was sickened by
the methods men employed to live and trade on
the river
.

For a blood-chilling
ring of terror to
the very sound
of his name was
the tool he needed for
the job he'd promised to do
.

Opposite
every gate was a hitching post or a stone carriage-step
, set
with a rusty iron
ring for tying a horse
.

When they were first written
, there was evidently no thought
of their being published
, and those which refer to
the writer's love for Mrs. Meynell particularly have
the ring of truth
.

Both abolition
of war and new techniques
of production
, particularly robot factories
, greatly increase
the world's wealth
, a situation described
in the following passage
, which has
the true utopian
ring: `` Everything was so cheap that
the necessities
of life were free
, provided as a public service by
the community
, as roads
, water
, street lighting and drainage had once been
.

Her mother
, now dead
, was my good friend and when she came to tell us about her plans and to show off her
ring I had a sobering wish to say something meaningful to her
, something her mother would wish said
.

One means to help
the birds occurs to me: Let
the chimes that
ring over Washington Square twice daily
, discontinue any piece
of music but one
.

The first shrill
ring of the telephone brought Harold out into
the hall
.

Hearing his voice
ring raucously up from
the road
, Kate would await him anxiously and watch perplexed as he walked into
the house
, cold sober
.

The morning hawk
, hungry for any eatable
, killable
, digestible item
, kept his eyes on
the ring of anchored ships that lay off
the shores
in the bay
, sheltered by
the Jersey inlets
.

When you and your dog step into
the Junior
ring, it should be just what
the dog wants to do as much as what you want him to do
.

Before
the Juniors entered
the ring the Steward announced that after all Juniors had moved their dogs around
the ring and set them up
, they could relax
with their dogs
.

As
the Juniors entered
the ring, Mr. Spring
, the announcer
, stated over
the public-address system that this was
the 28th year that Westminster has held
the Finals
of the Junior Competition
.

After
the judge moved all
the dogs individually
, she selected several from
the group and placed them
in the center
of the ring.

When directions read `` sl a marker on needle ''
, put a small safety pin
, paper clip
, or commercial
ring marker on needle
.

The energy received by
the `` pill '' causes
the resonant circuit to ``
ring '' on after
the burst and this `` ringing '' takes place at
the resonant frequency
of the `` pill ''
.
This gave her an opportunity to
ring down
the curtain
with the petulant admonition that we should not presume to lecture her on Abstraction
.
( Jelke later served 21 months when he was found guilty
of masterminding a
ring of high-priced call girls
.

Houston police got to know Diane two years ago when
the vice squad picked her up for questioning about a call girl
ring.

He dialed it and listened to it
ring ten times before he hung up
.

-- Vital secrets
of Britain's first atomic submarine
, the Dreadnought
, and
, by implication
, of the entire United States navy's still-building nuclear sub fleet
, were stolen by a London-based soviet spy
ring, secret service agents testified today
.

Just how many sub secrets were being handed over when
the ring, watched for six months
, was broken remained untold
.
0.075 seconds.