Endomorphisms Of Abelian Groups Research Articles

Rings with kernel inclusion quasiorder

Building on previous work for semigroups of functions and binary relations, we axiomatize structures consisting of endomorphisms of abelian groups equipped with composition, the usual pointwise operations, and the quasi-order of kernel inclusion. The resulting structures are associative rings enriched by a quasiorder satisfying a finite set of laws. More generally, we axiomatize the kernel inclusion quasi-order on the ring R induced by a right R-module, and we call the resulting abstract structures rings with ker-order. A characterisation of the possible ker-orders on a fixed ring is given in terms of certain families of its right ideals. The lattice of all ker-orders on the ring of rational integers is described.

Endomorphisms of abelian groups with small algebraic entropy

We study the endomorphisms ϕ of abelian groups G having a “small” algebraic entropy h (where “small” usually means h(ϕ)<log2). Using essentially elementary tools from linear algebra, we show that this study can be carried out in the group Qd, where an automorphism ϕ with h(ϕ)<log2 must have all eigenvalues in the open circle of radius 2, centered at 0 and ϕ must leave invariant a lattice in Qd, i.e., be essentially an automorphism of Zd. In particular, all eigenvalues of an automorphism ϕ with h(ϕ)=0 must be roots of unity. This is a particular case of a more general fact known as Algebraic Yuzvinskii Theorem. We discuss other particular cases of this fact and we give some applications of our main results.

Endomorphisms of abelian groups and the theorem of Baer and Kaplansky

Endomorphisms of abelian groups and the theorem of Baer and Kaplansky

Inner endomorphisms of Abelian groups

Inner endomorphisms of Abelian groups

Die Endomorphismenringe abelscher Gruppen und die Darstellung von Ringen durch Matrizenringe

Die Endomorphismenringe abelscher Gruppen und die Darstellung von Ringen durch Matrizenringe

O endomorfismech Abelových grup

O endomorfismech Abelových grup