Commuting rings of simple A(k)-modules

Biendomorphism rings of nitely presented simple modules

Commuting $pi$-regular rings

R is called commuting regular ring (resp. semigroup) if for each x,y $in$ R there exists a $in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting $pi$-regular rings (resp. semigroups) and study various properties of them.

Public Key Cryptography Based on Simple Modules over Simple Rings

The Diffie Hellman key exchange and the ElGamal oneway trapdoor function are the basic ingredients of public key cryptography. Both these protocols are based on the hardness of the discrete logarithm problem in a finite ring. In this paper we show how the action of a ring on a module gives rise to a generalized Diffie-Hellman and ElGamal protocol. This leads naturally to a cryptographic protoco...

Associated Graphs of Modules Over Commutative Rings

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between the algebraic properties of modules and their associated graphs. A topological characterization for the completeness of the special subgraphs is presented. Also modules whose associated graph is complete...

Endomorphism Rings of Modules over Prime Rings

Endomorphism rings of modules appear as the center of a ring, as the fix ring of a ring with group action or as the subring of constants of a derivation. This note discusses the question whether certain ∗-prime modules have a prime endomorphism ring. Several conditions are presented that guarantee the primeness of the endomorphism ring. The contours of a possible example of a ∗-prime module who...