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首页> 外文期刊>Journal of algebra and its applications >A CHARACTERIZATION OF THE COMMUTATIVE UNITAL RINGS WITH ONLY FINITELY MANY UNITAL SUBRINGS
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A CHARACTERIZATION OF THE COMMUTATIVE UNITAL RINGS WITH ONLY FINITELY MANY UNITAL SUBRINGS

机译：具有有限个微分环的交换环的刻画。

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A (commutative unital) ring is said to have FSP if it has only finitely many unital subrings. The singly generated rings that have FSP have been classified. Thus, a characterization of the rings satisfying FSP is obtained by proving that a ring R has FSP if and only if either R is finite or R = Z[t(1),..., t(n)] superset of Z where Z[t(i)] has FSP for each i = 1,..., n. Also, the following characterization is given for the nontrivial ring direct products Pi(i is an element of I) R-i that have FSP: I is finite, each R-i has FSP, and there is at most one i is an element of I such that R-i has characteristic 0.
机译：如果（交换单元）环只有有限的多个单元子环，则称其具有FSP。具有FSP的单​​个生成的环已被分类。因此，通过且仅当R为有限或R = Z [t（1），...，t（n）]的Z的超集时，证明环R具有FSP，才能获得满足FSP的环的特征。 Z [t（i）]对于每个i = 1，...，n具有FSP。同样，对具有平凡的空间的非平凡环直接积Pi（i是I的Ri）给出以下表征：I是有限的，每个Ri都具有FSP，并且最多有一个i是I的元素，使得Ri具有特征0。

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