On inverse skew Laurent series extensions of weakly rigid rings

摘要

Let R be a ring equipped with an automorphism and an -derivation . We studied on the relationship between the quasi Baerness and (, )-quasi Baerness of a ring R and these of the inverse skew Laurent series ring R((x(-1); , )), in case R is an (, )-weakly rigid ring. Also we proved that for a semicommutative (, )-weakly rigid ring R, R is Baer if and only if so is R((x(-1); , )). Moreover for an (, )-weakly rigid ring R, it is shown that the inverse skew Laurent series ring R((x(-1); , )) is left p.q.-Baer if and only if R is left p.q.-Baer and every countable subset of left semicentral idempotents of R has a generalized countable join in R.