EUDML

All rings considered in this paper are assumed to be commutative with identities. A ring $R$ is a $Q$ -ring if every ideal of $R$ is a finite product of primary ideals. An almost $Q$ -ring is a ring whose localization at every prime ideal is a $Q$ -ring. In this paper, we first prove that the statements, $R$ is an almost $Z P I$ -ring and $R [x]$ is an almost $Q$ -ring are equivalent for any ring $R$ . Then we prove that under the condition that every prime ideal of $R (x)$ is an extension of a prime ideal of $R$ , the ring $R$ is a (an almost)...

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On some properties of polynomial rings.

Two properties of the power series ring.

Exchange PF-rings and almost PP-rings.

Some properties of strongly normal lattices

Some properties of the ideal of continuous functions with pseudocompact support.

Characterizing symmetric diametrical graphs of order 12 and diameter 4.

Topological characterization of certain classes of lattices

Exchange PF-rings and almost PP-rings

Conditions under which $R (x)$ and $R 〈 x 〉$ are almost Q-rings