the concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. the notion of free fuzzy modules was introducedby muganda as an extension of free modules in the fuzzy context. zahedi and ameriintroduced the concept of projective and injective l-modules. in this paper we give analternate definition for projective l-modules. we prove that e...

We define natural A∞-transformations and construct A∞-category of A∞-functors. The notion of non-strict units in an A∞-category is introduced. The 2-category of (unital) A∞-categories, (unital) functors and transformations is described. The study of higher homotopy associativity conditions for topological spaces began with Stasheff’s article [Sta63, I]. In a sequel to this paper [Sta63, II] Sta...

Let A and C be two unital simple C*-algebras with tracial rank zero. Suppose that C is amenable and satisfies the Universal Coefficient Theorem. Denote by KKe(C,A) ++ the set of those κ for which κ(K0(C)+ \ {0}) ⊂ K0(A)+ \ {0} and κ([1C ]) = [1A]. Suppose that κ ∈ KKe(C,A) . We show that there is a unital monomorphism φ : C → A such that [φ] = κ. Suppose that C is a unital AH-algebra and λ : T(...

Abstract. When a unital C*-algebra A has topological stable rank one (write tsr(A) = 1), we know that tsr(pAp) ≤ 1 for a non-zero projection p ∈ A. When, however, tsr(A) ≥ 2, it is generally faluse. We prove that if a unital C*algebra A has a simple unital C*-subalgebra D of A with common unit such that D has Property (SP) and supp∈P (D) tsr(pAp) < ∞, then tsr(A) ≤ 2. As an application let A be...

We prove that under a mild hypothesis, the infinite tensor power of a unital separable C∗-algebra absorbs the Jiang–Su algebra Z tensorially. Combining this result with a recent theorem of Winter, we complete Elliott’s classification program for strongly self-absorbing ASH algebras. We also give a succinct universal property for Z in an ambient category so large that there are no unital separab...

Suppose that $${\mathscr {E}}$$ and {F}}$$ are Hilbert $$C^*$$ -modules. We present a power-norm $$\left( \left\| \cdot \right\| ^{{\mathscr {E}}}_n:n\in {\mathbb {N}}\right) $$ based on obtain some of its fundamental properties. introduce new definition the absolutely (2, 2)-summing operators from to , denote set such by $${\tilde{\Pi }}_2({\mathscr {E}},{\mathscr {F}})$$ with convention {E}})...

Let D and A be unital and separable C∗-algebras; let D be strongly selfabsorbing. It is known that any two unital ∗-homomorphisms from D to A ⊗ D are approximately unitarily equivalent. We show that, if D is also K1-injective, they are even asymptotically unitarily equivalent. This in particular implies that any unital endomorphism of D is asymptotically inner. Moreover, the space of automorphi...

LetX be a compact metric space and let Λ be a Z (k ≥ 1) action onX.We give a solution to a version of Voiculescu’s problem of AF-embedding: The crossed product C(X) ⋊Λ Z k can be embedded into a unital simple AF-algebra if and only if X admits a strictly positive Λ-invariant Borel probability measure. Let C be a unital AH-algebra, let G be a finitely generated abelian group and let Λ : G → Aut(...

We present a new construction of non-classical unitals from a classical unital U in PG(2, q2). The resulting non-classical unitals are B–M unitals. The idea is to find a non-standard model Π of PG(2, q2) with the following three properties: (i) points of Π are those of PG(2, q2); (ii) lines of Π are certain lines and conics of PG(2, q2); (iii) the points in U form a non-classical B–M unital in ...

Abstract Every finite subunital of any generalized hermitian unital is itself a unital; the embedding given by an quadratic field extensions. In particular, with one (i.e., it originates from separable extension).