On Endomorphisms of Normal Orthogroups

As well known, a normal orthogroup is a strong semilattice of rectangular groups. In this paper, we consider the homomorphisms between normal orthogroups and endomorphisms of themselves, relating them to the homomorphisms and endomorphisms of the underlying rect-angular groups with their compositions.

LEFT INVERSES AND RIGHT INVERSES OF A STRONG ENDOMORPHISM OF A GRAPH

In this paper, we characterize left inverses and right inverses of a strong endomorphism of a graph under some certain Green's equivalence conditions. In addition, the number of them is also given.

A construction of quasi-hereditary endomorphism algebras

In this article, we consider endomorphism algebras of direct sums of some local left ideals over a local algebra and give a construction of quasi-hereditary algebras.

On Primitive Idempotents of the Strong Endomorphism Monoid of a Graph

In this paper, we describe the canonical partial order on the idempotent set of the strong endomorphism monoid of a graph, and using this we further characterize primitive idem potenes from the viewpoint of combinatorics. The number of them is also given.

On Hochschild Homology of Endomorphism Algebras of Exceptional Sequences

In this note, we studied the Hochschild Homology of endomorphism algebras of exceptional sequences over any hereditary algebras.

Inverses of Regular Strong Endomorphisms of Graphs

In this paper we explicitly describe all the commuting pseudo inverses of a completely regular strong endomorphism of a graph from a viewpoint of combinatorics. The number of them is also given. In addition, a strong endomorphism of a graph, whose commuting pseudo inverse set coincides with its pseudo inverse set, is identified.

Split graphs whose half-strong endomorphisms form a monoid

In this paper, the half-strong, the locally strong and the quasi-strong endomorphisms of a split graph are investigated. Let X be a split graph and let End（X）, hEnd（X）, 1End（X） and qEnd（X） be the endomorphism monoid, the set of all half-strong endomorphisms, the set of all locally strong endomorphisms and the set of all quasi-strong endomorphisms of X, respectively. The conditions under which hEnd（X） forms a submonoid of End（X） are given. It is shown that 1End（X） = qEnd（X） for any split graph X. The conditions under which 1End（X） （resp. qEnd（X）） forms a submonoid of End（X） are also given. In particular, if hEnd（X） forms a monoid, then 1End（X） （resp. qEnd（X）） forms a monoid too.

Split Graphs with Completely Regular Endomorphism Monoids

In this paper, split graphs with complete endomorphism-regularity are characterized explicitly. Hopefully, the main idea of the proofs can also be used for other classes of graphs.

Shadowing and Inverse Shadowing for C^1 Endomorphisms

In this paper, we consider the shadowing and the inverse shadowing properties for C^1 endomorphisms. We show that near a hyperbolic set a C^1 endomorphism has the shadowing property, and a hyperbolic endomorphism has the inverse shadowing property with respect to a class of continuous methods. Moreover, each of these shadowing properties is also ＂uniform＂ with respect to C^1 perturbation.

An Extended Ockham Algebra with Endomorphism Kernel Property

An algebraic structure A is said to have the endomorphism kernel property if every congruence on A, other than the universal congruence, is the kernel of an endomorphism on A. In this paper, we consider the EKP （that is, endomorphism kernel property） for an extended Ockham algebra A. In particular, we describe the structure of the finite symmetric extended de Morgan algebras having EKP.

Finite Abelian Groups with the Strong Endomorphism Kernel Property

An endomorphism h of a group G is said to be strong whenever for every congruenceθon G,(x,y)∈θimplies(h(x),h(y))∈θfor every x,y∈G.A group G is said to have the strong endomorphism kernel property if every congruence on G is the kernel of a strong endomorphism.In this note,we study the strong endomorphism kernel property in the class of Abelian groups.In particular,we show that a finite Abelian group has the strong endomorphism kernel property if and only if it is cyclic.

Unstable manifolds for endomorphisms

A detailed presentation of an unstable manifold theorem for non invertible differentiable maps of finite dimensional manifolds is given.

Inverses and Pseudo-Inverses of a Strong Endomorphism of a Graph

In this paper,we explicitly describe all the inverses and pseudo-inverses of a strong endomorphism of a graph.The number of them is determined.In addition,we give a characterization of a strong endomorphism whose pseudo-inverse set coincides with its inverse set.The graph,each strong endomorphism of which has this property,is also investigated.

The Join of Split Graphs Whose Half-strong Endomorphisms Form a Monoid

In this paper, the half-strong endomorphisms of the join of split graphs are investigated. We give the conditions under which the half-strong endomorphisms of the join of split graphs form a monoid.

Classification of Special Anosov Endomorphisms of Nil-manifolds

In this paper we give a classification of special endomorphisms of nil-manifolds:Let f:N/Γ→N/Γbe a covering map of a nil-manifold and denote by A:N/Γ→N/Γthe nil-endomorphism which is homotopic to f.If f is a special TA-map,then A is a hyperbolic nil-endomorphism and f is topologically conjugate to A.

Existence of periodic points of endomorphisms of a circle

A theorem of Block and Franke is improved on the existence of periodic points for a map of a circle to itself and a proof which seems more understandable is given.

On Endomorphism Monoids of Finite Kleene Algebras

An endomorphism monoid of an algebra A.is said to be a band if every endomorphism on A is an idempotent,and it is said to be a demi-band if every noninject ive endomorphism on A is an idempotent.We precisely determine finite Kleene algebras whose endomorphism monoids are demi-bands and bands via Priestley duality.

ISOMORPHISMS BETWEEN ENDOMORPHISM RINGS OF FREE MODULES

In this paper we give the following main results: (ⅰ) Let F(?) and G(?) be two free modules. Then F(?) and G(?) are semi-linearly isomorphic if and only if End F(?) and End G(?) are strictly isomorphic. (ⅱ) We give a new method to generalize the Bolla theorem in 1985 which gave a categorical description for isomorphism between End F(?) and End G(?). (ⅲ) The Wolfson theorem is a corollary of our theorem.

Non-algebraic compact Khler threefolds admitting endomorphisms

We classify non-algebraic compact Khler threefolds admitting an endomorphism f:X → X of degree at least two.

On Robustness of Orbit Spaces for Partially Hyperbolic Endomorphisms

In this paper, the robustness of the orbit structure is investigated for a partially hyperbolic endomorphism f on a compact manifold M. It is first proved that the dynamical structure of its orbit space （the inverse limit space） M^f of f is topologically quasi-stable under C^0-small perturbations in the following sense： For any covering endomorphism g C^0-close to f, there is a continuous map φ from M^9 to Π-∞^∞ M such that for any {yi}i∈z∈φ（M^9）, yi＋1 and f（yi） differ only by a motion along the center direction. It is then proved that f has quasi-shadowing property in the following sense： For any pseudo-orbit {xi}i∈z, there is a sequence of points {yi}i∈z tracing it, in which yi＋1 is obtained from f（yi） by a motion along the center direction.