Digraphs associated with finite rings

Green's Symmetries in Finite Digraphs

The semigroup DV of digraphs on a set V of n labeled vertices is defined. It is shown that DV is faithfully represented by the semigroup Bn of n × n Boolean matrices and that the Green’s L, R, H, and D equivalence classifications of digraphs in DV follow directly from the Green’s classifications already established for Bn. The new results found from this are: (i) L, R, and H equivalent digraphs...

Digraphs of finite linear transformations

If T is a function from a finite set V to itself, we form the digraph D of T as follows. It has V for its vertex set, and there is an arc from x to T (x) for each x E V. Here we answer the following question. Given a finite field F, which digraphs arise as digraphs of a linear transformation from some finite dimensional vector space over F to itself?

Locally-finite connected-homogeneous digraphs

Modules with Dedekind Finite Endomorphism Rings

This article is a survey of modules whose endomorphism rings are Dedekind finite, Hopfian or co-Hopfian. We summarise the properties of such modules and present unified proofs of known results and generalisations to new structure theorems. MSC 2010. 16S50, 16D80.

Commutative Rings with Finite Quotient Fields

We consider the class of all commutative reduced rings for which there exists a finite subset T ⊂ A such that all projections on quotients by prime ideals of A are surjective when restricted to T . A complete structure theorem is given for this class of rings, and it is studied its relation with other finiteness conditions on the quotients of a ring over its prime ideals. Introduction Our aim i...