The maximal regular ideal of some commutative rings

Emad Abu Osba; Melvin Henriksen; Osama Alkam; Frank A. Smith

On rings close to regular and $p$ -injectivity

Roger Yue Chi Ming (2006)

Commentationes Mathematicae Universitatis Carolinae

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The following results are proved for a ring $A$ : (1) If $A$ is a fully right idempotent ring having a classical left quotient ring $Q$ which is right quasi-duo, then $Q$ is a strongly regular ring; (2) $A$ has a classical left quotient ring $Q$ which is a finite direct sum of division rings iff $A$ is a left $TC$ -ring having a reduced maximal right ideal and satisfying the maximum condition on left annihilators; (3) Let $A$ have the following properties: (a) each maximal left ideal of $A$ is either a two-sided...

Diagonal reductions of matrices over exchange ideals

Huanyin Chen (2006)

Czechoslovak Mathematical Journal

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In this paper, we introduce related comparability for exchange ideals. Let $I$ be an exchange ideal of a ring $R$ . If $I$ satisfies related comparability, then for any regular matrix $A \in M_{n} (I)$ , there exist left invertible $U_{1}, U_{2} \in M_{n} (R)$ and right invertible $V_{1}, V_{2} \in M_{n} (R)$ such that $U_{1} V_{1} A U_{2} V_{2} = diag (e_{1}, \dots, e_{n})$ for idempotents $e_{1}, \dots, e_{n} \in I$ .

Displaying similar documents to “The maximal regular ideal of some commutative rings”

On rings close to regular and p -injectivity

Diagonal reductions of matrices over exchange ideals

On rings close to regular and $p$ -injectivity