Locally m-pseudoconvex algebras

Several properties of advertibly complete locally m-pseudoconvex algebras are described. It is proved that a unital commutative locally m-pseudoconvex Hausdorff algebra is advertibly complete if and only if from a is an element of A and phi(a) not equal 1 for all phi is an element of hom A follows that a is an element of QinvA (respectively, from a is an element of A and phi(a) not equal 0 for all phi is an element of hom A follows that a is an element of InvA).