Topological characterization of certain classes of lattices
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 is a (an almost)...
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