Let (B, λt, ψ) be a C-dynamical system where (λt : t ∈ IT+) be a semigroup of injective endomorphism and ψ be an (λt) invariant state on the C ∗ subalgebra B and IT+ is either non-negative integers or real numbers. The central aim of this exposition is to find a useful criteria for the inductive limit state B →t B canonically associated with ψ to be pure. We achieve this by exploring the minima...

Injective one-way trapdoor functions are one of the most fundamental cryptographic primitives. In this work we show how to derandomize lossy encryption (with long messages) to obtain lossy trapdoor functions, and hence injective one-way trapdoor functions. Bellare, Halevi, Sahai and Vadhan (CRYPTO ’98) showed that if Enc is an IND-CPA secure cryptosystem, and H is a random oracle, then x 7→ Enc...

The concept of generalized path algebras was introduced in Coelho and Liu (Lecture Notes Pure Appl. Math. 210, 53–66, 2000). Roughly speaking, these are constructed a way similar to that over quiver, the difference being we assign an algebra each vertex quiver consider paths intercalated with elements from algebras. Then use concatenation together structure define multiplication. representation...

Semigroups S for which the Banach algebra ℓ 1 (S) is injective are investigated and an application to the work of O. Yu. Aristov is described.

We study classes of modules over a commutative ring which allow to do homological algebra relative to such a class. We classify those classes consisting of injective modules by certain subsets of ideals. When the ring is Noetherian the subsets are precisely the generization closed subsets of the spectrum of the ring.

The local multiplier C*-algebra Mloc(A) of any C*-algebra A can be ∗-isomorphicly embedded into the injective envelope I(A) of A in such a way that the canonical embeddings of A into both these C*-algebras are identified. If A is commutative then Mloc(A) ≡ I(A). The injective envelopes of A and Mloc(A) always coincide, and every higher order local multiplier C*-algebra of A is contained in the ...

An injective $k$-edge-coloring of a graph $G$ is an assignment colors, i.e. integers in $\{1, \ldots , k\}$, to the edges such that any two each incident with one distinct endpoint third edge, receive colors. The problem determining whether $k$-coloring exists called k-INJECTIVE EDGE-COLORING. We show 3-INJECTIVE EDGE-COLORING NP-complete, even for triangle-free cubic graphs, planar subcubic gr...

This paper characterizes the injective and projective objects in the category of directed multigraphs, or quivers. Further, the injective envelope and projective cover of any quiver in this category is constructed.

Let $R$ be a commutative ring with identity. The purpose of this paper is to introduce and study two classes of modules over $R$, called $mbox{Max}$-injective and $mbox{Max}$-strongly top modules and explore some of their basic properties. Our concern is to extend some properties of $X$-injective and strongly top modules to these classes of modules and obtain some related results.

We investigate and compare four variants of the doublepushout approach to graph transformation. Besides the traditional approach with arbitrary matching and injective right-hand morphisms, we consider three variations by employing injective matching and/or arbitrary right-hand morphisms in rules. For each of the three variations, we clarify whether the well-known commutativity theorems are stil...