Abstract
π-complemented algebras are defined as those (not necessarily associative or unital) algebras such that each annihilator ideal is complemented by other annihilator ideal. For a given semiprime algebra A, we discuss the π-complementation of the unitisation algebra A 1 of A. Moreover, if in addition the multiplication algebra ℳ(A) of A is also semiprime, we study the π-complementation in the algebras ℳ(A) and ℳ♯(A) (the multiplication ideal of A). In associative setting, we prove that A is π-complemented if and only if ℳ♯(A) is π-complemented, and that A 1 π-complemented if and only if ℳ(A) is π-complemented.
2010 Mathematics Subject Classification:
ACKNOWLEDGMENT
Partially supported by Junta de Andalucía grant FQM 0290 and Project MTM2009-12067.
Notes
Communicated by M. Bresar.