In this paper we answer a question raised in [Mol] by giving an example of a proper standard C∗-subalgebra of B(H) whose automorphism and isometry groups are topologically reflexive. After this we prove that in the case of extensions of the C∗-algebra C(H) of all compact operators by separable commutative C∗algebras, these groups are algebraically reflexive. Concerning the most well-known exten...

Let K be a field and X an m×n matrix of indeterminates over K. Let K[X] denote the polynomial ring generated by all the indeterminates Xij . For a given positive integer r ≤ min{m, n}, we consider the determinantal ideal Ir+1 = Ir+1(X) generated by all r + 1 minors of X if r < min{m, n} and Ir+1 = (0) otherwise. Let Rr+1 = Rr+1(X) be the determinantal ring K[X]/Ir+1. Determinantal ideals and ri...

A Gram-Schmidt type algorithm is given for finite d-dimensional reflexive forms over division rings. The algorithm uses d/3 + O(d) ring operations. Next, that algorithm is adapted in two new directions. First a sequential algorithm is given whose complexity matches the complexity of matrix multiplication. Second, a parallel NC algorithm is given with similar complexity.

Inclines are additively idempotent semi rings in which products are less than or equal to either factor.The Characterization of EP elements, Product of EP elements in an incline with involution are obtained as a generalization and development of EP elements in a *regular ring and of EP elements in a reflexive semi group. Mathematics Subject Classification: 16Y60, 15A09

In this paper, the notions of anti-reflexive kernel, symmetric kernel, reflexive closure, and symmetric closure of a soft set relation are first introduced, respectively. Then, their accurate calculation formulae and some properties are obtained. Finally, soft set relation mappings and inverse soft set relationmappings are proposed, and some related properties are discussed. © 2010 Elsevier Ltd...

Let 1 < q < p < ∞ and q ≤ r ≤ p. Let X be a reflexive Banach space satisfying a lower-lq-tree estimate and let T be a bounded linear operator from X which satisfies an upper-lp-tree estimate. Then T factors through a subspace of ( ∑ Fn)lr , where (Fn) is a sequence of finite-dimensional spaces. In particular, T factors through a subspace of a reflexive space with an (lp, lq) FDD. Similarly, let...

For a self-small abelian group A of torsion-free rank 1, we characterize A-reflexive abelian groups which are induced by the contravariant functor Hom(−, A) in two cases: the range of Hom(−, A) is the category of all abelian groups, respectively the range of Hom(−, A) is the category of all left E-modules, where E is the endomorphism ring of A.

It has recently been shown that a minimal reversible nonsymmetric ring order 256 answering question originally posed in paper on taxonomy of 2-primal rings. In different work, questions rings having to do with this were also answered. work it is abelian reflexive nonsemicommutative 256, related left open these previous works. here [Formula: see text] such ring. This consequence the main result ...