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ArticleSethuraman, BharathFor each prime p and each n ≥ 1 (n ≥ 2 if p = 2), examples are constructed of a Galois extension K∕F whose Galois group has exponent pn and a central simple Falgebra A of exponent p which is split by K but is not in the Dec group of K∕F.

ArticleKumar, K. RajFor the quasistatic, Rayleighfading multipleinput multipleoutput (MIMO) channel with transmit and receive antennas, Zheng and Tse showed that there exists a fundamental tradeoff between diversity and spatialmultiplexing gains, referred to as the . . .

ArticleSivic, KlemenWe show that for all $ k\ge 1$ there exists an integer $ N(k)$ such that for all $ n\ge N(k)$ the $ k$th order jet scheme over the commuting $ n\times n$ matrix pairs scheme is reducible. At the other end of the spectrum, it is known that for all $ k . . .

ArticleJonov, BoyanWe consider the affine variety Zm,n2,2 of firstorder jets over Zm,n2, where Zm,n2 is the classical determinantal variety given by the vanishing of all 2×2 minors of a generic m×n matrix. When 2<m≤n, this jet scheme Zm,n2,2 has two irreducible compone . . .

ArticleSethuraman, BharathWe present some general techniques for constructing fullrank, minimaldelay, rate at least one spacetime block codes (STBCs) over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras (field extension . . .

ArticleGuralnick, Robert M.In this note, we show that the set of all commuting dtuples of commuting n×n matrices that are contained in an ndimensional commutative algebra is a closed set, and therefore, Gerstenhaber's theorem on commuting pairs of matrices is a consequence of . . .

ArticleSethuraman, BharathLet F be a Henselian valued field with char(F) =/2, and let S be an inertially split Fcentral division algebra with involution sigma* that is trivial on an inertial lift in S of the field Z(S). We prove necessary and sufficient conditions for S to co . . .

ArticleSethuraman, BharathWe study components and dimensions of higherorder determinantal varieties obtained by considering generic m×n (m⩽n) matrices over rings of the form F[t]/(tk), and for some fixed r, setting the coefficients of powers of t of all r×r minors to zero. Th . . .

ArticleBounds On Fast Decodability Of SpaceTime Block Codes, SkewHermitian Matrices, And Azumaya AlgebrasMarkin, NadyaWe study fast lattice decodability of spacetime block codes for n transmit and receive antennas, written very generally as a linear combination Σi=12l si Ai, where the si are real information symbols and the Ai are n×n ℝlinearly independent complex . . .
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