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ON COMMUTATIVE GELFAND RINGS | ||
| Journal of Sciences, Islamic Republic of Iran | ||
| مقاله 8، دوره 10، شماره 3، آذر 1999 اصل مقاله (241.34 K) | ||
| چکیده | ||
| A ring is called a Gelfand ring (pm ring ) if each prime ideal is contained in a unique maximal ideal. For a Gelfand ring R with Jacobson radical zero, we show that the following are equivalent: (1) R is Artinian; (2) R is Noetherian; (3) R has a finite Goldie dimension; (4) Every maximal ideal is generated by an idempotent; (5) Max (R) is finite. We also give the following resu1ts:an ideal of R is uniform, if and only if, it is a minimal ideal; Ass (R) is exactly the set of all maximal ideals which are generated by an idempotent element of R | ||
| عنوان مقاله [English] | ||
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| چکیده [English] | ||
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