Conditions under which $R(x)$ and $R\langle x\rangle $ are almost Q-rings

Hani A. Khashan; H. Al-Ezeh

Displaying similar documents to “Conditions under which $R (x)$ and $R 〈 x 〉$ are almost Q-rings”

When is every order ideal a ring ideal?

Melvin Henriksen, Suzanne Larson, Frank A. Smith (1991)

Commentationes Mathematicae Universitatis Carolinae

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A lattice-ordered ring $ℝ$ is called an if each of its order ideals is a ring ideal. Generalizing earlier work of Basly and Triki, OIRI-rings are characterized as those $f$ -rings $ℝ$ such that $ℝ / 𝕀$ is contained in an $f$ -ring with an identity element that is a strong order unit for some nil $l$ -ideal $𝕀$ of $ℝ$ . In particular, if $P (ℝ)$ denotes the set of nilpotent elements of the $f$ -ring $ℝ$ , then $ℝ$ is an OIRI-ring if and only if $ℝ / P (ℝ)$ is contained in an $f$ -ring with an identity element that is a strong order unit. ...

Minimal prime ideals of skew polynomial rings and near pseudo-valuation rings

Vijay Kumar Bhat (2013)

Czechoslovak Mathematical Journal

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Let $R$ be a ring. We recall that $R$ is called a near pseudo-valuation ring if every minimal prime ideal of $R$ is strongly prime. Let now $σ$ be an automorphism of $R$ and $δ$ a $σ$ -derivation of $R$ . Then $R$ is said to be an almost $δ$ -divided ring if every minimal prime ideal of $R$ is $δ$ -divided. Let $R$ be a Noetherian ring which is also an algebra over $ℚ$ ( $ℚ$ is the field of rational numbers). Let $σ$ be an automorphism of $R$ such that $R$ is a $σ (*)$ -ring and $δ$ a $σ$ -derivation of $R$ such that $σ (δ (a)) = δ (σ (a))$ for all $a \in R$ . Further,...

Two new types of rings constructed from quasiprime ideals.

Ghanem, Manal, Al-Ezeh, Hassan (2011)

International Journal of Mathematics and Mathematical Sciences

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Displaying similar documents to “Conditions under which R ( x ) and R 〈 x 〉 are almost Q-rings”

When is every order ideal a ring ideal?

Minimal prime ideals of skew polynomial rings and near pseudo-valuation rings

Two new types of rings constructed from quasiprime ideals.

Displaying similar documents to “Conditions under which $R (x)$ and $R 〈 x 〉$ are almost Q-rings”