Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 13185-768, Tehran, Iran.
In this paper we investigate some hereditary properties of amenability modulo an
ideal of Banach algebras. We show that if (e) is a bounded approximate identity modulo I
of a Banach algebra A and X is a neo-unital modulo I, then (e) is a bounded approximate
identity for X. Moreover we show that amenability modulo an ideal of a Banach algebra A
can be only considered by the neo-unital modulo I Banach algebra over A.