Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-Invariant Maximal Subfields and Their Connexion with Some
  Conjectures in Division Rings   Let D be a division algebra with center F. A maximal subfield of D is defined
to be a field K such that CD(K) = K; that is, K is its own centralizer in D. A
maximal subfield K is said to be self-invariant if it normalises by itself,
i.e. ND*(K)= K: This kind of subfields is important because they have strong
connexion with the most famous Albert's Conjecture (every division ring of
prime index is cyclic). In fact, we pose a question that asserts whether every
division ring whose all maximal subfields are self-invariant has to be
commutative. The positive answer to this question, in finite dimensional case,
implies the Albert's Conjecture (see x2). Although we show the Mal'cev-Neumann
division ring demonstrates negative answer in the case of infinite dimensional
division rings, but it is still most likely the question receives positive
answer if we restrict ourselves to the finite dimensional division rings. We
also have had the opportunity to use the Mal'cev-Neumann structure to answer
Conjecture 1 below in negative (see x3). Finally, among other things, we rely
on this kind of subfields to present a criteria for a division ring to have
finite dimensional subdivision ring (see x4).

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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat