Let R be a local ring of prime characteristic. We study the ring of Frobenius operators F(E), where E is the injective hull of the residue field of R. In particular, we examine the finite generation of F(E) over its degree zero component F0(E), and show that F(E) need not be finitely generated when R is a determinantal ring; nonetheless, we obtain concrete descriptions of F(E) in good generalit...

This paper is an exposition of the so-called injective Morita contexts (in which the connecting bimodule morphisms are injective) and Morita α-contexts (in which the connecting bimodules enjoy some local projectivity in the sense of ZimmermannHuisgen). Motivated by situations in which only one trace ideal is in action, or the compatibility between the bimodule morphisms is not needed, we introd...

An injective coloring of graphs is a vertex coloring where two vertices receive distinct colors if they have a common neighbor. In 1977, Wegner [12] posed a conjecture on the chromatic number of squares of graphs which remains unsolved for planar graphs with maximum degrees ∆ ≥ 4. Obviously, the chromatic number of the square of a graph is at least the injective chromatic number of a graph. We ...

A realization of a graph G is pair (G,p) where p maps the vertices into Euclidean space Rd. The injective if and quasi-injective for each edge G, endpoints to different points in space. globally rigid any (G,q) Rd with same lengths congruent (G,p). In this paper we characterize graphs that have an (quasi-injective, respectively) non-globally R1, show problem recognizing these NP-complete both c...

A ring R is called right א0-injective if every right homomorphism from a countably generated right ideal of R to RR can be extended to a homomorphism from RR to RR. In this note, some characterizations of א0-injective rings are given. It is proved that if R is semiperfect, then R is right א0injective if and only if every homomorphism from a countably generated small right ideal of R to RR can b...

Nakayama (Ann. of Math. 42, 1941) showed that over an artinian serial ring every module is a direct sum of uniserial modules. Hence artinian serial rings have the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals. A ring with the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals will be called a ...

We present a satisfiability-preserving embedding of coalition logic into a normal modal logic. An advantage of standard, normal, modal logics is a well understood theoretical foundation and the availability of tools for automated verification and reasoning. The target logic is multi-modal K with intersection of modalities, interpreted over standard Kripke models corresponding to game structures...

Injective one-way trapdoor functions are one of the most fundamental cryptographic primitives. In this work we give a novel construction of injective trapdoor functions based on oblivious transfer for long strings. Our main result is to show that any 2-message statistically sender-private semihonest oblivious transfer (OT) for strings longer than the sender randomness implies the existence of i...

Let S be a closed orientable surface of genus at least two, and let C be an arbitrary (complex) projective structure on S. We show that there is a decomposition of S into pairs of pants and cylinders such that the restriction of C to each component has an injective developing map and a discrete and faithful holonomy representation. This decomposition implies that every projective structure can ...