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On hereditarily linearly compact algebras. (English)
Authors: Bordan V. G., Ursul M. I.
Abstract
It is introduced the notion of a hereditarily linearly compact algebra. It is proved that semisimple hereditarily linearly compact algebras are exactly topological products of infinite dimensional division algebras and matrix algebras over finite dimensional division algebras (theorem 9). The Jacobson radical of a hereditarily linearly compact algebra is bounded and topologically nilpotent (theorem 8). It is given the complete characterization of those fields $F$ for which every hereditarily linearly compact $F$-algebra is strongly linearly compact (theorem 11).Institutul de Matematică Academia de Ştiinţe a Moldovei
str. Academiei 5, Chişinău MD-2028, Moldova
str. Academiei 5, Chişinău MD-2028, Moldova
Contents
- Concordant solutions of quasilinear multidimensional differential equations. (Russian)
- Combinatorial formula for generalized Fibonacci sequence and Chebyshev's polynomials of two variables. (English)
- Properties of topological modules free in some classes. II. (English)
- Global attractors of infinite-dimensional dynamical systems. II. (Russian)
- On hereditarily linearly compact algebras. (English)
- A generalized coupled dynamic problem of thermoelasticity for plane, cylindrical and spherical media. (Russian)
- Three-dimensional point groups of simple and double $P$- and $(P/)$-antisymmetry and their geometric applications. (Russian)
- Comparison of some sufficient conditions for smooth linearization. (English)
- On reduced right ideals of a ring. (English)
- Some properties of left quasihomomorphic mappings. (Russian)
- On three-dimensional hyperbolic manifolds with icosahedral symmetry. (Russian)
- Affine invariant conditions for topological classification of quadratic systems with $m_f=1$. (English)
