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.

We extend the Ahlbrandt–Ziegler analysis of interpretability in א0-categorical structures by showing that existential interpretation is controlled by the monoid of self–embeddings and positive existential interpretation of structures without constant endomorphisms is controlled by the monoid of endomorphisms in the same way as general interpretability is controlled by the automorphism group.

We start with a modular K-system that possesses Anosov endomorphisms in both time directions. We extend the system via a crossed product construction. If one of the Anosov endomorphisms can be extended, then also the other one. Also the extensions form a Moebius group and allow a time reeection operator that implements on the algebra an antiisomorphism.

We introduce the universal functorial Lefschetz invariant for endomorphisms of finite CW -complexes in terms of Grothendieck groups of endomorphisms of finitely generated free modules. It encompasses invariants like Lefschetz number, its generalization to the Lefschetz invariant, Nielsen number and L2-torsion of mapping tori. We examine its behaviour under fibrations.

We introduce endomorphisms of special jacobians and show that they satisfy polynomial equations with all integer roots which we compute. The eigen-abelian varieties for these endomorphisms are generalizations of Prym-Tyurin varieties and naturally contain special curves representing cohomology classes which are not expected to be represented by curves in generic abelian varieties.

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.

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

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...

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.