We prove that the ring of endomorphisms of the ℘-divisible group of a Drinfeld module of characteristic ℘ is canonically isomorphic to the ring of endomorphisms of the underlying Drinfeld module, completed in the ℘–adic topology. This completes the proof of the Tate Conjectures in the Drinfeld module setting.

The notion of ring endomorphisms having large images is introduced. Among others, injectivity and surjectivity of such endomorphisms are studied. It is proved, in particular, that an endomorphism σ of a prime one-sided noetherian ringR is injective whenever the image σ(R) contains an essential left ideal L of R. If additionally σ(L) = L, then σ is an automorphism of R. Examples showing that the...

Endomorphisms of the measure algebra commutative hypergroups are investigated. We focus on derivations and higher order which closely related to moment function sequences rank. describe exact connection between those endomorphisms if it is considered as a module over ring continuous functions.

Cohn called a ring $R$ is reversible if whenever $ab = 0,$ then $ba = 0$ for $a,bin R.$ The reversible property is an important role in noncommutative ring theory‎. ‎Recently‎, ‎Abdul-Jabbar et al‎. ‎studied the reversible ring property on nilpotent elements‎, ‎introducing‎ the concept of commutativity of nilpotent elements at zero (simply‎, ‎a CNZ ring)‎. ‎In this paper‎, ‎we extend the CNZ pr...

In the study of pre-Lie algebras, concept pre-morphism arises naturally as a generalization standard notion morphism. Pre-morphisms can be defined for arbitrary (not-necessarily associative) algebras over any commutative ring k with identity, and dualized in various ways to generalized morphisms (related pre-Jordan algebras) anti-pre-morphisms anti-pre-Lie algebras). We consider idempotent pre-...

Let ℧ be a prime ring of char(℧) ≠2 with its center Z. This article introduces new classes endomorphisms and investigates how they relate to antiautomorphisms rings the commutativity rings. Additionally, we fully describe classify some these endomorphisms. We also give examples prove necessity numerous restrictions included in hypotheses our results.

Summary We formalize in the Mizar system [3], [4] some basic properties on left module over a ring such as constructing via of endomorphism an abelian group and set all homomorphisms modules form [1] along with Ch. 2 set. 1 [2]. The formalized items are shown below list notations: M ab for Abelian suffix “ ” without is used ring. 1. denoted by End ( ). 2. A pair homomorphism <m:math xmlns:m="ht...

We study the interplay between canonical heights and endomorphisms of an abelian variety A over a number field k. In particular we show that whenever the ring of endomorphisms defined over k is strictly larger than Z there will be Q-linear relations among the values of a canonical height pairing evaluated at a basis modulo torsion of A(k).1

A ring or an idempotent semiring is associative provided that additive endomorphisms are multiplicative.