We first note that affine quasi-heredity is a Morita invariant between

unital algebras.

Wang, "Reduced free products of

unital AH algebras and Blackadar and Kirchberg's MF algebras," The Journal of Operator Theory, vol.

Regarding globalization, one of the most important recent results can be found in reference [4], in which the notion of Morita equivalence between partial actions was given and it was proved that every partial group action over a not necessarily

unital algebra is Morita equivalent to a globalizable (

unital) partial action.

Let U be

unital, and let [phi] : U [right arrow] C be a nonzero BJH.

Semirings satisfy all properties of

unital rings except the existence of additive inverses.

In [25] it is proved using Theorem 4.1 that kB is

unital if and only if B is connected and, moreover, the [DELTA]([B.sub.[greater than or equal to]X]) are all acyclic in this case.

(2) we propose two key updating methods for the

unital design based key management scheme.

In what follows, we will only consider

unital [C.sup.*]-algebras.

According to one of their results [1, Theorem 20], any surjective norm-linear map between uniform algebras which satisfies some other quite weak properties is a composition operator and, therefore, is an isometric

unital algebra isomorphism.

For n [greater than or equal to] 0, define the quantum polynomial ring [A.sup.(q).sub.n] to be the

unital noncommutative Z[[q.sup.[+ or -]1/2]]-algebra generated by the [n.sup.2] variables x = [([x.sub.i,j]).sub.1[less than or equal to]i,j[less than or equal to]n] and subject to the relations

In this note, we introduce a generalized trace from a *-ideal I of a

unital [C.sup.*]-algebra A into a

unital Abelian [C.sup.*]-algebra B and prove some properties on it.

Following [9], Nandor Sieben in [11] defined the crossed product of a [C.sup.*]-algebra and a

unital inverse semigroup by an action [beta] .