Abstract:In this paper, a combination of algebraic and topological methods are applied to obtain new and structural results on harmonic rings. Especially, it is shown that if a Gelfand ring A modulo its Jacobson radical is a zero dimensional ring, then A is a clean ring. It is also proved that, for a given Gelfand ring A, then the retraction map Spec(A) → Max(A) is flat continuous if and only if A modulo its Jacobson radical is a zero dimensional ring. Dually, it is proved that for a given mp-ring A, then the retractio… Show more
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