splitting field meaning in Tamil

Tamil words for splitting field

பிளக்கும் வெளி

English meaning of splitting field

1. noun (of a polynomial) Given a polynomial p over a field K, the smallest extension field L of K such that p, as a polynomial over L, decomposes into linear factors (polynomials of degree 1); (of a set of polynomials) given a set P of polynomials over K, the smallest extension field of K over which every polynomial in P decomposes into linear factors.
2. noun Given a finite-dimensional K-algebra (algebra over a field), an extension field whose every simple (indecomposable) module is absolutely simple (remains simple after the scalar field has been extended to said extension field).
3. noun Given a central simple algebra A over a field K, another field, E, such that the tensor product A⊗E is isomorphic to a matrix ring over E.
4. noun (of a character χ of a representation of a group G) A field K over which a K-representation of G exists which includes the character χ; (of a group G) a field over which a K-representation of G exists which includes every irreducible character in G.

Full definition of splitting field

splitting field in a sentence

• Every finite dimensional central simple algebra has a splitting field: moreover, if said CSA is a division algebra, then a maximal subfield of it is a splitting field.

Synonyms of splitting field

• root field

Questions about splitting field in Tamil

What is the meaning of splitting field in Tamil?

Splitting field in Tamil is பிளக்கும் வெளி.

splitting field என்பதன் தமிழ் அர்த்தம் என்ன?

Splitting field: பிளக்கும் வெளி.

What does splitting field mean in English?

Splitting field means (of a polynomial) Given a polynomial p over a field K, the smallest extension field L of K such that p, as a polynomial over L, decomposes into linear factors (polynomials of degree 1); (of a set of polynomials) given a set P of polynomials over K, the smallest extension field of K over which every polynomial in P decomposes into linear factors.