广义幂级数环的主拟Baer性

摘要

Let R be a ring such that all left semicentral idempotents are central and(S, ≤) a strictly totally ordered monoid satisfying that 0 ≤ s for all s ∈ S. It is shown that [[RS, ≤]], the ring of generalized power series with coefficients in R and exponents in S, is right p.q. Baer if and only if R is right p.q. Baer and any S-indexed subset of I(R) has a generalized join in I(R), where I(R) is the set of all idempotents of R.