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On the property of a right ideal of a ring to be two-sided. (Russian)
Authors: Andrunakievich A. V.
Abstract
The assiciative ring $R$ not obligatory with a unity is considered. Let $P\triangleleft R_R$ a fully reduced right ideal, i.e. $a^2Q\Longrightarrow a\in Q$, where $a\in R$, $Q\triangleleft R_R$, $Q\supseteq P$. If for any $r\in R$ there is $P$-idempotent $e\in R$, i.e. $e\notin P$, $e^2 e\in P$, $eP\subseteq P$ and for $Q\triangleleft R_R$, $Q\supseteq P$ implication takes place, $e\notin Q\Longrightarrow r\in Q$, $P$ is proved to be a two - sided ideal.Institutul de Matematică Academia de Ştiinţe a Moldovei
str. Academiei 5, MD-2028 Chişinău, Moldova
str. Academiei 5, MD-2028 Chişinău, Moldova
Contents
- Approximate solution of singular integral equations with the help of series with respect to Faber-Laurent polynomials. (Russian)
- Global attractors of infinite-dimensional dynamical systems. I. (Russian)
- β-acyclic schemes of databases. (Romanian)
- Methods of derivation of semi-minor and pseudo-minor groups of $W$-symmetry. (Russian)
- On primitive solvable permutation groups with commutative stabilizer of a point. II. (Russian)
- Finite generated subalgebras of free CHQ-algebra. (English)
- Submodules determined by cohereditary radicals. (English)
- On strongly regular near-rings. (English)
- Impact of viscoelastic rod upon an obstacle. (Russian)
- On the property of a right ideal of a ring to be two-sided. (Russian)
- Energy saving in agro-food complex. (English)
- Impact of an elastic rod of finite length upon a compliant obstacle. II. (Russian)
- On automorphism groups of left-distributive quasigroups. (Russian)
- Torsion theories and subcategories of divisible modules. (English)
- Generating functions for comitants of differential systems. (Russian)
