involution of a ring

In this paper we have given some results about involutive rings, and have proved that the residue classring Z[i]/(α) is an involutive ring if and only if α follows Gauss integer number: 1+i, (1+i)~2.

讨论了对合环,给出并证明了Gauss整数环Z[i]中模α的剩余类环Z[i]/(α)为对合环的充要条件。

We show that rings with a proper involution are semi-prime ring and algebra with proper involution is semi-prime algebra.

研究了正对合环的典型例子和若干性质,得出正对合环是半素环,从而证出带有正对合的代数是半素代数,从而改进了Kaplansky的结论。