Sammanhängande ring

Inom matematiken är en sammanhängande ring en kommutativ ring A som satisfierar ett följande ekvivalenta krav:[1]

Exempel

Sammanhängande ringarna bildar en ganska stor delmängd av ringar. Alla lokala ringar. Speciellt är alla integritetsområden sammanhängande. Ett exempel på en ring som inte är sammanhängande är Z × Z, där elementet (1, 0) är en icke-trivial idempotent.

Generaliseringar

Inom algebraisk geometri är sammanhängdhet relaterat till konceptet sammanhängande schema.

Källor

Den här artikeln är helt eller delvis baserad på material från engelskspråkiga Wikipedia, Connected ring, 28 februari 2015.
  • Jacobson, Nathan (1989), Basic algebra. II (2), New York: W. H. Freeman and Company, s. xviii+686, ISBN 0-7167-1933-9 
  1. ^ Jacobson 1989, p 418.

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