In this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $Z_{2}$. We also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

‎In this paper‎, ‎we propose some Diffie-Hellman type key exchange protocols using isogenies of elliptic curves‎. ‎The first method which uses the endomorphism ring of an ordinary elliptic curve $ E $‎, ‎is a straightforward generalization of elliptic curve Diffie-Hellman key exchange‎. ‎The method uses commutativity of the endomorphism ring $ End(E) $‎. ‎Then using dual isogenies‎, ‎we propose...

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...

let r be a ring,  be an endomorphism of r and mr be a -rigid module. amodule mr is called quasi-baer if the right annihilator of a principal submodule of r isgenerated by an idempotent. it is shown that an r-module mr is a quasi-baer module if andonly if m[[x]] is a quasi-baer module over the skew power series ring r[[x; ]].

A seminear-ring is a generalization of ring. In ring theory, if with the multiplicative identity, then endomorphism module isomorphic to . Let be seminear-ring. Here, we can construct set from itself denoted by We show that seminear-ring, also over addition and composition function. will apply congruence relation get quotient endomorphism. Furthermore, between c-ideal relations. So, c-ideal.

The object of this paper is to study the relationship between certain projective modules and their endomorphism rings. Specifically, the basic problem is to describe the projective modules whose endomorphism rings are (von Neumann) regular, local semiperfect, or left perfect. Call a projective module regular if every cyclic submodule is a direct summand. Thus a ring is a regular module if it is...

For a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-Armendariz ring, that is a generalization of both $pi$-Armendariz rings, and $(alpha,delta)$-compatible skew Armendariz rings. We first observe the basic properties of skew $pi$-Armendariz rings, and extend the class of skew $pi$-Armendariz rings through various ring extensions. We nex...

for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

We consider the endomorphism ring computation problem for supersingular elliptic curves, constructive versions of Deuring’s correspondence, and the security of Charles-Goren-Lauter’s cryptographic hash function. We show that constructing Deuring’s correspondence is easy in one direction and equivalent to the endomorphism ring computation problem in the other direction. We also provide a collisi...