Graded-division algebras over arbitrary fields

Triangular Uhf Algebras over Arbitrary Fields

Let K be an arbitrary field. Let (qn) be a sequence of positive integers, and let there be given a family \f¥nm\n > m} of unital Kmonomorphisms *F„m. Tqm(K) —► Tq„(K) such that *¥np*¥pm = %im whenever m < n , where Tq„ (K) is the if-algebra of all q„ x q„ upper triangular matrices over K. A triangular UHF (TUHF) K-algebra is any Kalgebra that is A'-isomorphic to an algebraic inductive limit of ...

Algebras of Minimal Rank over Arbitrary Fields

Let R(A) denote the rank (also called bilinear complexity) of a nite dimensional associative algebra A. A fundamental lower bound for R(A) is the so-called Alder{Strassen bound R(A) 2 dim A?t, where t is the number of maximal twosided ideals of A. The class of algebras for which the Alder{Strassen bound is sharp, the so-called algebras of minimal rank, has received a wide attention in algebraic...

Nicely semiramified division algebras over Henselian fields

We recall that a nicely semiramified division algebra is defined to be a defectless finitedimensional valued central division algebra D over a field E with inertial and totally ramified radical-type (TRRT) maximal subfields [7, Definition, page 149]. Equivalent statements to this definition were given in [7, Theorem 4.4] when the field E is Henselian. These division algebras, as claimed in [7, ...

Triangulaizability of Algebras Over Division Rings

Correspondences between Valued Division Algebras and Graded Division Algebras

If D is a tame central division algebra over a Henselian valued field F , then the valuation on D yields an associated graded ring GD which is a graded division ring and is also central and graded simple over GF . After proving some properties of graded central simple algebras over a graded field (including a cohomological characterization of its graded Brauer group), it is proved that the map ...