Let E be a B-complete (B -complete) locally convex algebra and $ the
topological direct sum of countably many copies of the scalar field with a
jointly continuous algebra multiplication. It has been shown that E is also
B-complete (B -complete) for componentwise multiplication on E . B-and
Br-completeness of E , the unitization of E, and also of E x for other
multiplications on E has been studied.