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...

the minimal prime decomposition for semiprime ideals is defined and studied on z-ideals of c(x). the necessary and sufficient condition for existence of the minimal prime decomposition of a z-ideal / is given, when / satisfies one of the following conditions: (i) / is an intersection of maximal ideals. (ii) i is an intersection of o , s, when x is basically disconnected. (iii) i=o , when x x ha...

Abstract. In the table of multivariate rational interpolants the entries are arranged such that the row index indicates the number of numerator coefficients and the column index the number of denominator coefficients. If the homogeneous system of linear equations defining the denominator coefficients has maximal rank, then the rational interpolant can be represented as a quotient of determinant...

We determine structure and multiplicative complexity of commutative group algebras over algebraically closed fields. Commutative group algebra A of dimension n over algebraically closed field is isomorphic to B, where B is a superbasic algebra of minimal rank (see [5] for definition), and t is maximal that t | n, p t. Multiplicative and bilinear complexity of A equal to 2n − t.