【摘要】 <正>I1和I2分别是环R的一个左理想和右理想,T1=R[x]和T2=R[x,x-1]分别表示多项式环和洛朗多项式环.首先给出两个例子,分别说明了T1I1不一定是T1的左理想与T2I2不一定是T2的右理想.其次给出了环的多项式扩张及洛朗扩张的理想的性质.最后证明了,若R[x](R[x,x-1])是拟-Baer环,则R也是拟-Baer环.更多还原

【Abstract】 I1 and I2 be a left ideal and a right ideal of the ring R respectively,T1=R[x] and T2=R[x,x-1]be a polynomial ring and a Laurent polynomial ring respectively.Firstly,the thesis provides two examplesexplaining that T1I1 is not necessarily a left ideal of T1 and T2I2 is not necessarily a right ideal of T2.Secondly,it proves the properties of ideals on polynomial extensions and Laurent extensions of rings by which we showthat R is a quasi-Baer ring if R[x](R[x,x-1]) is a quasi-Baer ring.更多还原