Conditions under which and are almost Q-rings
Hani A. Khashan, H. Al-Ezeh (2007)
Archivum Mathematicum
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All rings considered in this paper are assumed to be commutative with identities. A ring is a -ring if every ideal of is a finite product of primary ideals. An almost -ring is a ring whose localization at every prime ideal is a -ring. In this paper, we first prove that the statements, is an almost -ring and is an almost -ring are equivalent for any ring . Then we prove that under the condition that every prime ideal of is an extension of a prime ideal of , the ring ...