同时，还证明了半直和的剩余类环是整环的一个整扩张。

An integral extension construction of domains was also derived by using the semi-direct sum of rings.

youdao

但是到处人们都在死于胃溃疡，或者将他们的胃整个或一半切除；在我们的周围，永久性的切除术和死亡一直都在发生。

But people died from ulcers all over the place and were having their stomachs or half their stomachs removed; there were permanent, mutilating operations and deaths going on around us.

youdao

进一步，如果S是半素环，那么M的每个极大核是M的一个直和项。

Further, if S is a semiprime ring, then every maximal kernel of M is a direct summand of M.

youdao