Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
On reduced right ideals of a ring. (English)
Authors: Andrunakievich V. A., Reabuhin Iuri
Abstract
In the work we study reduced right ideals $P$ of a ring $R$ (i.e. $r^2\in P\Rightarrow r\in P$). It is demonstrate that if $P$ is a strongly reduced ideal (i.e. ewery right ideal $T\supseteq P$ is reduced), then $P$ is a bilateral ideal of $R$ and $R/P$ is a strongly (or abelian) regular ring. As the corollary we obtain a criterion of the decomposition of a ring $R$ to the subdirect product of division rings.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)
