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We call a field E a splitting field for A if A ⊗ E is isomorphic to a matrix ring over E. Every finite dimensional CSA has a splitting field: indeed, in the case when A is a division algebra, then a maximal subfield of A is a splitting field.
Some Related Sentences
We and call
We should spread the view that planning and national development are serious matters which call for effort as well as enthusiasm.
We have only to think of Lady Macbeth or the policeman-murderer in Thomas Burke's famous story, `` The Hands Of Mr. Ottermole '', to realize that hands often call up ideas of crime and punishment.
Why, man, that's the same kind of music we've been playin ' since 1928 !... We didn't call it rock and roll back when we introduced it as our style back in 1928, and we don't call it rock and roll the way we play it now.
Attlee responded the next day in the debate on increased air estimates that Hitler's speech contained unfavourable references to the Soviet Union but that " We see here a chance to call a halt in the armaments race ... We do not think that our answer to Herr Hitler should be just rearmament.
We will call the first the furnace and the second the refrigerator .” Carnot then explains how we can obtain motive power, i. e. “ work ”, by carrying a certain quantity of heat from body A to body B.
In 1945, Engelbart had read with interest Vannevar Bush's article " As We May Think ", a call to action for making knowledge widely available as a national peacetime grand challenge.
* " We shot music, call it murder on the dancefloor, and we got more bars than wandsworth and dartmoor "-Dartmoor Prison, mentioned in Devlin's song Shot Music ( May 10, 2010 )
Let us call the class of all such formulas R. We are faced with proving that every formula in R is either refutable or satisfiable.
:" We worship ," replied Hengist, " our country gods, Saturn and Jupiter, and the other deities that govern the world, but especially Mercury, whom in our language we call Woden and to whom our ancestors consecrated the fourth day of the week, still called after his name Wodensday.
Savoy dancer " Shorty " George Snowden stated that " We used to call the basic step the Hop long before Lindbergh did his hop across the Atlantic.
We may represent any given proposition with a letter which we call a propositional constant, analogous to representing a number by a letter in mathematics, for instance,.
We understand that shows don't want to call the writers writers because they want to maintain the illusion that it is reality, that stuff just happens.
We and field
We do not favor one field over another: we think that all inquiry, all scholarly and artistic creation, is good -- provided only that it contributes to a sense and understanding of the true ends of life, as all first-rate scholarship and artistic creation does.
We can do this through the characteristic values and vectors of T in certain special cases, i.e., when the minimal polynomial for T factors over the scalar field F into a product of distinct monic polynomials of degree 1.
We might not see any rotation initially, but if we closely look at the right, we see a larger field at, say, x = 4 than at x = 3.
We have evidence that Jupiter has a magnetic field and that birds are oviparous, but as of yet, we do not seem to have found evidence of moral properties, such as " goodness ".
We have previously mentioned that there can be more than one way of indexing the degrees of freedom in a quantum field.
) We can construct field operators by applying the Fourier transform to the creation and annihilation operators for these states.
We take the velocity field associated with this current as the velocity field whose integral curves yield the motion of the particle.
We conclude that, in the field of public education, the doctrine of " separate but equal " has no place.
We provide a sketch of a proof for the case where the underlying field of scalars is the complex numbers.
We have, therefore, directed the Irish Army authorities to have field hospitals established in County Donegal adjacent to Derry and at other points along the Border where they may be necessary.
( We developed ) a theory to explain how solar protons can diffuse inward and gain energy in the Earth's magnetic field.
We now recognise this as part of the ideal class group: in fact Kummer had isolated the p-torsion in that group for the field of p-roots of unity, for any prime number p, as the reason for the failure of the standard method of attack on the Fermat problem ( see regular prime ).
We can assume that A contains ¬ φ, the field axioms, and, for some k, the first k sentences of the form 1 + 1 +...+ 1 ≠ 0 ( because adding more sentences doesn't change unsatisfiability ).
We can construct a classical continuous random field that has the same probability density as the quantum vacuum state, so that the principal difference from quantum field theory is the measurement theory ( measurement in quantum theory is different from measurement for a classical continuous random field, in that classical measurements are always mutually compatible — in quantum mechanical terms they always commute ).
We assume that the underlying field is not of characteristic 2: that is, that where 1 denotes the multiplicative identity and 0 the additive identity of the given field.
We claim that, as a field, the quotient is isomorphic to the complex numbers, C. A general complex number is of the form, where a and b are real numbers and Addition and multiplication are given by