About: Connected ring

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In mathematics, especially in the field of commutative algebra, a connected ring is a commutative ring A that satisfies one of the following equivalent conditions: * A possesses no non-trivial (that is, not equal to 1 or 0) idempotent elements; * the spectrum of A with the Zariski topology is a connected space.

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  • In mathematics, especially in the field of commutative algebra, a connected ring is a commutative ring A that satisfies one of the following equivalent conditions: * A possesses no non-trivial (that is, not equal to 1 or 0) idempotent elements; * the spectrum of A with the Zariski topology is a connected space. (en)
  • Inom matematiken är en sammanhängande ring en kommutativ ring A som satisfierar ett följande ekvivalenta krav: * A har inga icke-triviala (d.v.s. andra än 1 och 0) * Spektret av A med Zariskitopologin är ett sammanhängande rum. (sv)
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  • In mathematics, especially in the field of commutative algebra, a connected ring is a commutative ring A that satisfies one of the following equivalent conditions: * A possesses no non-trivial (that is, not equal to 1 or 0) idempotent elements; * the spectrum of A with the Zariski topology is a connected space. (en)
  • Inom matematiken är en sammanhängande ring en kommutativ ring A som satisfierar ett följande ekvivalenta krav: * A har inga icke-triviala (d.v.s. andra än 1 och 0) * Spektret av A med Zariskitopologin är ett sammanhängande rum. (sv)
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  • Connected ring (en)
  • Sammanhängande ring (sv)
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