Recognition of division algebras

Triangulaizability of Algebras Over Division Rings

On normalizers of maximal subfields of division algebras

‎Here‎, ‎we investigate a conjecture posed by Amiri and Ariannejad claiming‎ ‎that if every maximal subfield of a division ring $D$ has trivial normalizer‎, ‎then $D$ is commutative‎. ‎Using Amitsur classification of‎ ‎finite subgroups of division rings‎, ‎it is essentially shown that if‎ ‎$D$ is finite dimensional over its center then it contains a maximal‎ ‎subfield with non-trivial normalize...

INITIAL RAMIFICATION INDEX OF NONINVARIANT VALUATIONS ON FINITE DIMENSIONAL DIVISION ALGEBRAS

Let D be a division ring with centre K and dim, D< ? a valuation on K and v a noninvariant extension of ? to D. We define the initial ramfication index of v over ?, ?(v/ ?) .Let A be a valuation ring of o with maximal ideal m, and v , v ,…, v noninvariant extensions of w to D with valuation rings A , A ,…, A . If B= A , it is shown that the following conditions are equivalent: (i) B i...

ON SELBERG-TYPE SQUARE MATRICES INTEGRALS

In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are defined under the abstract algebra. Then Selberg-type integrals are calculated under orthogonal transformations.

Nondegenerate semiramified valued and graded division algebras

In this paper, we define what we call (non)degenerate valued and graded division algebras [Definition 3.1] and use them to give examples of division p-algebras that are not tensor product of cyclic algebras [Corollary 3.17] and examples of indecomposable division algebras of prime exponent [Theorem 5.2, Corollary 5.3 and Remark 5.5]. We give also, many results concerning subfields of these divi...