abstract. let r be a 2-torsion free ring with identity. in this paper, first we prove that any jordan left derivation (hence, any left derivation) on the full matrix ringmn(r) (n  2) is identically zero, and any generalized left derivation on this ring is a right centralizer. next, we show that if r is also a prime ring and n  1, then any jordan left derivation on the ring tn(r) of all n×n up...

In this paper we prove that the image of multilinear polynomials evaluated on algebra UTn(K) n × upper triangular matrices over an infinite field K equals Jr, a power its Jacobson ideal J = J(UTn(K)). particular, shows analogue Lvov—Kaplansky conjecture for is true, solving Fagundes and de Mello. To fact, introduce notion commutator-degree polynomial characterize r in terms coefficients. It tur...

This paper concerns the enumeration of simultaneous conjugacy classes [Formula: see text]-tuples commuting matrices in upper triangular group text] and unitriangular over finite field odd characteristic. is done for text], by computing branching rules. Further, using matrix thus computed, we explicitly get probabilities each case.

Building upon the application of flags to network coding introduced in [6], we develop a variant this technique that uses degenerate flags. The information set is metric affine space isometric upper triangular matrices endowed with flag rank metric. This suggests development theory for codes analogy used linear subspace coding.

We present a variation of Paige's algorithm for computing the generalized singular value decomposition (GSVD) of two matrices A and B. There are two innovations. The rst is a new preprocessing step which reduces A and B to upper triangular forms satisfying certain rank conditions. The second is a new 2 by 2 triangular GSVD algorithm, which constitutes the inner loop of Paige's algorithm. We pre...