Ih this paper we introduce idempotently decreasing sequences and i—bounded compact sets such that they provide a set of equivelent propertions about i bounologieal algebra. Further we havr studied the algebra k[x]. It is an i—bornological algebra under the locally m—convex topology Jx. Hence on and algebra E it naturally produces an i—bornological algebra

the intrinsic i—bornological algebra as I call it. In §3

we obtain the condition of an i—bounded set t0 be a subalgebra (0)

and a sufficient condition for a locally m—convex algebra t0 be an i—bornolegical algebra on E.