关于PMM环

定义了PMM环．环R称为PMM环，若对任何Morita相似于R的环S，存在m，n∈N，使得Mm(S)同构于Mn(R)．证明了如下结果：环R是PMM环当且仅当任给R的投射生成元P，存在m，n∈N，以及R上的Picard投射生成元Q，使得Pm同构于Qn．具有VBN性质的PMM环是T2-环；具有IBN性质的PM环是T1-环．若交换环R是PMM环，则R是不可分解的且R的Picard群是幂可除的．特别地，Dedekind整环R是PMM环当且仅当R的Picard群是幂可除的．

On PMM Rings

The PMM rings are defined and studied in this paper.A ring R is called a PMM ring if for any ring S which is Morita similar to R,Mm(S) is isomorphic to Mn(R) for some n,m∈N. The following results are proved in this paper.A ring R is a PMM ring if and only if whenever given a progenerator P over R, there exist m,n∈N and some Picard progenerator Q over R such that Pm is isomorphic to Qn. PMM rings with VBN property are just T2-rings;and with IBN property are T1-rings.If R is a commutative PMM ring,then R is indecomposable and the Picard group of R is power divisible.In particular,a Dedekind domain R is a PMM ring if and only if the Picard group of R is power divisible.