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* There is a one-to-one correspondence between the two-sided ideals of M < sub > n </ sub >( R ) and the two-sided ideals of R. Namely, for each ideal I of R, the set of all n × n matrices with entries in I is an ideal of M < sub > n </ sub >( R ), and each ideal of M < sub > n </ sub >( R ) arises in this way.
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Some Related Sentences
There and is
`` There isn't anything left to say, is there, Keith ''??
There was a measure of protection in its concrete walls and ceiling, but the engineers who hastily installed it were well aware that concrete is not much better than prayer, if as efficacious, when a direct hit comes along.
There is nothing for you '', Matsuo said.
There is much truth in both these charges, and not many Bourbons deny them.
There is unceasing pressure, but its sources are immediate.
There is little time for the men in the command centers to reflect about the implications of these clocks.
There is no room for error or waste.
There is a New South emerging, a South losing the folksy traditions of an agrarian society with the rapidity of an avalanche -- especially within recent decades.
There is a haunting resemblance between the notion of cause in Copernicus and in Freud.
There is still the remote possibility of planetoid collision.
There is the unexplainable, and there art raises questions that it does not attempt to answer ''.
There is nothing holy in wedlock.
There is no more `` plot '' than that ; ;
There is a legend ( Hawthorne records it in his `` English Notebooks ''.
It consists of fragmentary personal revelations, such as `` The Spark '': `` There is a spark dwells deep within my soul.
There is only one catch to this idyllic arrangement: Adam Smith was wrong.
Harris J. Griston, in Shaking The Dust From Shakespeare ( 216 ), writes: `` There is not a word spoken by Shylock which one would expect from a real Jew ''.
There is no justification for such misrepresentation.
There is no socially existential answer to the question.
There is no selectivity ; ;
There is probably some significance in the fact that two of the best incest stories I have encountered in recent years are burlesques of the incest myth.
There is no necessity, I suppose, to assert that Mr. Faulkner is Southern.
There is evidence to suggest, in fact, that many authors of the humorous sketches were prompted to write them -- or to make them as indelicate as they are -- by way of protesting against the artificial refinements which had come to dominate the polite letters of the South.
There may be a case of this sort, but it is not one we wish to argue, here.
There and one-to-one
There is a one-to-one correspondence between the base units of mechanics in CGS and SI, and the laws of mechanics are not affected by the choice of units.
There is a one-to-one correspondence between the occupation number representation and valid boson states in the Fock space.
There is a one-to-one correspondence between the number of buckets and the number of values that can be represented by a digit.
There is a one-to-one correspondence between the free variables of the predicate and the attribute names of the relation heading.
There is no one-to-one correspondence between Germanic and Celtic gods.
There is a natural one-to-one correspondence between multilinear maps
There is a distinct fundamental cycle for each edge ; thus, there is a one-to-one correspondence between fundamental cycles and edges not in the spanning tree.
There is no one-to-one mapping of MTP Levels 1 through 3 onto the OSI model.
There are five pattern matching operations other than a strict one-to-one match between the pattern and the source to be checked for a match.
There is no direct link, or one-to-one relationship, between every instance of helping behavior and a specific gain for the organization.
There are some caveats, though, the major one being we don't have a true one-to-one correspondence between the dual configuration spaces.
There is not always a one-to-one correspondence between the two methods of classifying substances.
There is one-to-one antilinear correspondence between continuous linear functionals and vectors.
There is a one-to-one correspondence between idempotent elements of a semigroup and maximal subgroups of the semigroup: each idempotent element is the identity element of a unique maximal subgroup.
There is one-to-one correspondence between Theban and the letters in the old Latin alphabet.
There is no strict one-to-one relationship between titles and works — What a Girl Wants is, unrelatedly, a Christina Aguilera song and an Amanda Bynes movie, while the first Harry Potter book is known both as Harry Potter and the Philosopher's Stone and Harry Potter and the Sorcerer's Stone.
There are 11 function rooms, ranging in size to accommodate every type of event, from one-to-one interviews to larger conferences, weddings and meetings for up to 350 guests.
The integral curve starting at the identity is a one-parameter subgroup of G. There are one-to-one correspondences
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